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How  TO  TEACH. 


GRADED  COURSE  OF  INSTRUCTION 


MANUAL   OF    METHODS 


USE     OF    TEACHERS. 


BY 
HENRY  KIDDLE,  A.M.. 

SUPERINTENDENT   OF   PUBLIC  INSTRUCTION,   NEW   YORK  CITY. 

THOMAS  F.  HARRISON, 

FIRST    ASSISTANT  SUPERINTENDENT  OF  GRAM.  SCHOOLS,   N.  Y.    CITY,   AND    PROF.    OF 
METHODS  AND  PRINCIPLES  OF  TEACHING   IN   SATURDAY  NORMAL  SCHOOL. 

N.  A.  CALKINS, 

FIRST  ASSISTANT  SUPERINTENDENT  OF   PRIM.    SCHOOLS,   N.  Y.   CITY,   AND    PROF.    Or 
METHODS  AND  PRINCIPLES  OF  TEACHING   IN  SATURDAY  NORMAL  SCHOOL. 


REVISED    EDITION. 


NEW-YORK      •:•      CINCINNATI      •:•     CHICAGO 

AMERICAN    BOOK    COMPANY 


Eclectic  Educational  Series. 


TEACHERS'  MANUALS, 


Kriisfs  Life  of  Pestalozzi. 
Hailmarfs  Kindergarten  Culture. 
Hailmati's  Lectures  on  History  of  Pedagogy. 
The  Examiner,  or  Teacher's  Aid. 
Smarts  Manual  of  Free  Gymnastics. 
Object  Lessons,  by  Lilienthal  and  Allyn. 
Payne 's  School  Supervision. 
Cow's  Good  Morals  and  Gentle  Manners. 


Copyright,  1872  and  1874,  by  J.  W.  SCHERMERHORN  &  Co. 
Copyright,  1877,  by  VAN  ANTWERP,  BRAGG  &  Co. 


fJrtntcb  at 
tTbe  Eclectic  press 
Cincinnati,  a.  s.  a 


Education 
library 

LB 


PREFACE. 


THE  system  of  graded  instruction,  which  has  become 
so  general  in  this  country,  requires  for  its  successful 
application,  the  constant  use,  on  the  part  of  the  teacher, 
of  a  guide,  or  chart,  to  which  he  may  refer  in  order 
that  his  present  work  may  harmonize  with  that  which 
preceded,  and  that  which  is  to  follow  it.  The  ground 
to  be  covered  in  a  complete  course  of  school  education, 
however  elementary,  is  quite  extensive,  and  hence  needs 
to  be  divided  and  subdivided  according  to  certain  estab- 
lished principles,  so  that  the  mind  of  the  instructor  may 
not  be  diverted  from  that  which  should  engage  his  im- 
mediate attention,  by  the  necessity  of  considering  and 
choosing  the  best  means  of  supplementing  it.  Such  a 
graded  system  of  teaching  can  best  be  prepared  by  those 
who  have  had  not  only  a  long  experience  in  the  practi- 
cal business  of  teaching,  but  whose  field  of  observation 
has  been  sufficiently  comprehensive  to  enable  them  to 
give  to  the  scheme  an  adaptability  to  a  great  variety  of 
circumstances. 

The  system  laid  down  in  the  work  here  offered  to 
practical  educators,  whether  teachers,  superintendents, 
or  school  officers,  is  designed  to  afford  such  a  guide  as 


4  PREFACE. 

is  above  indicated.  It  is  essentially  the  system  which 
has  been  in  use  in  the  city  of  New  York  for  some  years, 
only  differing  from  it  in  the  number  of  grades  into 
which  the  course  is  divided.  This  difference  is,  how- 
ever, rather  nominal  than  real,  since  the  number  of 
grades  into  which  a  course  of  study  is  divided  is  en- 
tirely arbitrary,  except  so  far  as  it  may  be  dictated  by 
special  circumstances.  Where  schools  are  very  large, 
and  the  attendance  of  pupils  is  fluctuating,  as  must  be 
the  case  in  so  populous  a  city  as  New  York,  the  neces- 
sity of  constantly  reorganizing  classes,  renders  frequent 
promotions,  or  transfers  from  class  to  class,  indispensa- 
ble, and,  hence,  a  large  number  of  grades  becomes  a 
convenience.  In  schools  having  a  smaller  and  steadier 
attendance,  the  number  of  grades  need  not  exceed  what 
is  requisite  for  a  proper  classification  and  division  of 
subjects  for  simultaneous  study.  The  order  of  studies 
— the  main  point  in  every  course  of  instruction — cor- 
responds, as  here  arranged,  precisely  with  the  New  York 
plan  ;  the  time  requisite  for  its  completion  is  also  about 
the  same. 

This  course,  with  its  division  into  grades,  constitutes, 
however,  only  the  frame-work  for  the  series  of  practical 
suggestions  designed  to  assist  teachers  in  the  perform- 
ance of  their  professional  duties — that  is,  in  some  de- 
gree, to  show  them  what  to  teach,  as  well  as  how  to  teach. 
All  the  precepts  and  directions  here  given  have  been 
dictated  by  an  earnest  desire  to  aid  in  the  effort  now 
universally  put  forth  by  the  ablest  and  most  intelligent 


PREFACE.  5 

school  officers  to  abolish  the  pernicious  rote  method  of 
teaching,  by  book  and  formula,  formerly  so  prevalent, 
and  to  make  universal  the  system  which  appeals,  from 
first  to  last,  to  the  intelligence  of  the  pupil,  and  adapts 
itself  to  its  progressive  stages  of  development.  In  the 
lower  grades,  the  objective,  or  perceptive,  system  is,  of 
course,  made  prominent,  to  be  succeeded  by  those  sub- 
jects and  methods  which,  as  they  dispense  to  a  consid- 
erable extent  with  the  actual  objects  themselves,  and 
appeal  to  the  acquired  ideas  of  the  pupils,  may  be  prop- 
erly denominated  conceptive. 

The  natural  and  physical  sciences,  it  will  be  observed, 
are  largely  drawn  upon  for  the  materials  necessary  to 
accomplish  this  object,  the  sciences  of  observation  and 
classification,  such  as  zoology,  botany,  and  mineralogy, 
properly  taking  precedence  of  those  which  require  a 
more  special  application  of  the  reflective  and  reasoning 
faculties,  such  as  physiology,  natural  philosophy,  and 
astronomy.  By  this  kind  of  teaching,  it  is  designed 
that  the  pupil  shall  acquire  the  ability  to  gain  an  ex- 
perience of  his  own,  instead  of  depending  exclusively 
upon  that  of  others,  and  at  the  same  time,  shall  acquire 
a  taste  for  the  observation  and  study  of  nature. 

Certainly  such  a  system  for  the  common  schools  of 
our  country  is  far  preferable  to  that  which,  although 
insuring  proficiency  in  the  "three  R's"  left  the  pupil's 
mind  in  a  condition  of  matured  stolidity,  and  while, 
perhaps,  a  most  ready  talking,  writing,  and  parsing  ma- 
chine, sent  him  forth  to  go  through  this  beautiful  world, 


(;  PREFACE. 

blind  to  its  manifold  wonders  and  glories,  and  fit  only 
to  become  the  easy  prey  of  the  demagogue  and  the 
bigot. 

It  is  an  evidence  of  the  increasing  earnestness  of 
teachers,  that  the  demand  for  practical  suggestions 
and  exact  information  in  regard  to  their  Avork  is  now  so 
great.  More  especially  is  this  so  in  the  case  of  those 
engaged  in  primary  school  instruction.  This  depart- 
ment of  teaching  requires  very  much  special  knowledge 
as  well  as  peculiar  tact  to  produce  successful  results. 
A  complete  exposition  of  the  various  methods  which 
are  applicable  to  each  stage  of  this  work  would  require 
a  much  larger  space  than  could  be  devoted  to  it  in  the 
book  here  published.  Hence,  references  to  more  full 
and  complete  works  on  the  subject  have  been  given  in 
connection  with  several  of  the  grades,  in  order  to  aid 
teachers  in  finding  the  additional  information  which 
they  may  need  in  this  direction. 

The  demand  for  copies  of  the  "  Manual  of  Instruc- 
tion and  Discipline,"  recently  prepared  by  the  authors 
of  this  work,  for  the  use  of  the  primary  and  grammar 
schools  of  the  city  of  New  York,  has  induced  them  to 
endeavor  to  put  the  work  into  a  shape  in  which  it  might 
be  generally  useful ;  and  they  trust  that,  as  it  is  now 
presented  to  those  engaged  in  practical  education,  it 
will  prove  an  acceptable  addition  to  the  literature  of 
American  pedagogy,  now  so  scanty  and  insufficient. 


CONTENTS. 


too* 

INTRODUCTION..  11 


GRADED  COURSE.— TENTH  GRADE  (Outline) 21 

How  TO  TEACH  SUBJECTS  OF  THE  TENTH  GRADE.  . .      23 
Reading  (23) ;    Phonetics  (27) ;  Spelling  (27) ;  Arith- 
metic (29) ;    Object    Lessons   (34) ;    Drawing  and 
Writing  (35)  ;  Management  (36). 

NINTH  GRADE  (Outline)..   37 

How  TO  TEACH  SUBJECTS  OF  THE  NINTH  GRADE...      39 
Reading  (39) ;  Phonetics  (40) ;  Definitions  (40) ;  Spell- 
ing (41) ;    Arithmetic  (41) ;    Object   Lessons   (44) ; 
Drawing  and  Writing  (45) ;  Management  (45). 

EIGHTH  GRADE  (Outline) 47 

How  TO  TEACH  SUBJECTS  OF  THE  EIGHTH  GRADE.  .      49 
Reading  (49) ;  Punctuation  (50)  ;  Phonetics  (50) ;  Def- 
initions (51) ;  Spelling  (51)  ;  Arithmetic  (52) ;  Object 
Lessons  (59) ;  Drawing  and  Writing  (61) ;  Manage- 
ment (62). 


8  CONTENTS. 

PAGE 

SEVENTH  GRADE  (Outline) 63 

How  TO  TEACH  SUBJECTS  OF  THE  SEVENTH  GRADE.       65 

Reading  (65) ;  Phonetics  (66)  ;  Definitions  (66) ;  Arith- 
metic (67) ;  Tables  (73) ;  Object  Lessons  (74) ;  Ge- 
ography— Preparatory  Steps  (80) ;  Drawing  and 
Writing  (81) 

SIXTH  GRADE  (Outline) 83 

How  TO  TEACH  SUBJECTS  OP  THE  SIXTH  GRADE  ...      86 
Reading  (86) ;  Phonetics  (87) ;  Definitions  (87) ;  Spell- 
ing (88) ;  Arithmetic  (88) ;  Tables  (92) ;  Object  Les- 
sons (94) ;  Geography  (98) ;  Drawing  and  Writing 
(102)  ;  General  Suggestions  (102). 

FIFTH  GRADE   (Outline) 105 

How  TO  TEACH  SUBJECTS  OF  THE  FIFTH  GRADE  . . .     107 
Reading  (107)  ;    Spelling   (110)  ;   Definitions    (111) ; 
Arithmetic  (113) ;  Forms  of  Arithmetical  Analysis 
(118)  ;  Tables  (120) ;  Geography— General  Sugges- 
tions (121);  Geography  for  the  Fifth  Grade  (122) ; 
•   Syllabus  of  Topics  for  Geography  (123) ;  Correction 
of  Language  (125) ;  Elementary  Science — General 
Suggestions  (126)  ;  Outlines  of  Zoology  (129). 

FOURTH  GRADE  (Outline) 137 

How  TO  TEACH  SUBJECTS  OP  THE  FOURTH  GRADE..     139 
Reading  (139)  ;  Spelling  (139) ;  Definitions  (140);  Eng- 
lish Grammar  (140)  ;   Arithmetic  (144)  ;  Syllabus 
of  Topics  for  Common  Fractions  (147);  Syllabus 


CONTENTS.  9 

PAOK 

for  Decimal  Fractions  (158) ;  Geography  (163) ;  Ele- 
mentary Science — Botany  (164) ;  Mineralogy  (168) ; 
Writing  (172)S. 

THIRD  GRADE  (Outline) 175 

How  TO  TEACH  SUBJECTS  OF  THE  THIRD  GRADE.  . .  177 
Reading  (177) ;  Spelling  (178) ;  English  Grammar 
(173);  Composition  (179) ;  Arithmetic  (180) ;  Sylla- 
bus for  Arithmetic  (182) ;  Geography  (186) ;  History 
of  the  United  States — General  Suggestions  (189) ; 
Outline  Sketch  of  the  History  of  the  United 
States  (189) ;  Syllabus  of  Topics  (193) ;  Physiology 
and  Hygiene  (194)  ;  Syllabus  for  Physiology  (196). 

SECOND  GRADE  (Outline) 199 

How  TO  TEACH  SUBJECTS  OP  THE  SECOND  GRADE.  .  201 
Reading  (201) ;  Definitions  and  Word  Analysis  (202) ; 
English  Grammar  (204) ;  Composition  (206) ;  Arith- 
metic (206) ;  Syllabus  for  Arithmetic  (209) ;  Geog- 
raphy (210)  ;  History  (211)  ;  Elementary  Science — 
Natural  Philosophy  (216) ;  Syllabus  of  Topics  (220) ; 
Astronomy  (221). 

FIRST  GRADE  (Outline) 223 

How  TO  TEACH  SUBJECTS  OP  THE  FIRST  GRADE 225 

English  Grammar  (225);  Composition  (226);  Arith- 
metic (226) ;  Algebra  (229) ;  Geometry  (232) ;  Out- 
lines of  Physical  Geography  (236) ;  History,  Ancient 
and  Modern  (238);  Natural  Philosophy  (241); 
Astronomy  (243) ;  Chemistry  (245) ;  Book-keeping 
(250)  ;  Constitution  of  the  United  States  (251). 


10  CONTENTS. 

PAGE 

GENERAL    SUGGESTIONS    RELATIVE    TO    CLASSI. 

FICATION  AND  INSTRUCTION 252 

Reviews  (252) ;  Progress  of  Classes  (252) ;  Progress 
of  Pupils  (252);  Recitations  (253);  Lessons  for 
Home  Study  (254);  Physical  Training  (255);  Man- 
ners  and  Morals  (256). 

GOVERNMENT  AND  DISCIPLINE 257 

SCHOOL  LIBRARY..  263 


INTKODUCTICXN". 


No  task  can  be  more  responsible,  or  require  the  exer- 
cise of  greater  care  than  that  which  has  for  its  object 
the  proper  education  of  the  young.  To  perform  it  effi- 
ciently, special  preparation  and  study  are  indispen- 
sably necessary,  not  only  in  regard  to  the  branches  of 
knowledge  which  may  have  been  selected  as  a  basis  for 
the  instruction,  but  also  in  respect  to  the  proper  methods 
and  appliances  to  be  employed,  in  order  to  render  the 
instruction  truly  effective.  These  methods  must  be 
determined  by  a  consideration  of  the  faculties  to  be 
trained  and  educated,  as  well  as  the  nature  of  the 
subject  taught ;  hence,  the  teacher  should  be  familiar 
witb  at  least  the  outlines  of  mental  science, — the  office 
of  each  of  the  faculties  of  the  mind,  the  order  in  which 
they  are  naturally  developed,  and  the  proper  means  of 
aiding  in  this  development,  so  that  the  training  and  in- 
struction given  may  result  in  that  most  valuable  of  all 
characteristics,  a  well-balanced  mind.  It  is  the  remark 
of  Professor  Henry,  that  "the  laws  which  govern  the 
growth  and  operations  of  the  human  mind  are  as  defi- 
nite, and  as  general  in  their  application,  as  those  which 
apply  to  the  material  universe  ;  and  it  is  evident  that  a 
true  system  of  education  must  be  based  upon  a  knowl- 
edge and  application  of  those  laws."  How  important 
then  that  the  teacher  should  make  himself  familiar  with 
these  laws !  Certainly  no  true  success  can  be  obtained 


12  INTRODUCTION. 

without  this  knowledge  ;  for  destitute  of  it,  the  teacher 
is  only  an  empiric,  applying  rules  the  reason  of  which 
he  does  not  know,  and  mechanically  following  methods, 
the  rationale  of  which  he  does  not  understand. 

If  the  teacher  have  sufficiently  mastered  these  elemen- 
tary principles  of  his  profession,  it  will  not  be  difficult 
for  him  at  all  times  rightly  to  understand  his  pupils' 
mental  condition  and  grade  of  advancement — a  matter 
of  the  greatest  importance,  especially  at  the  first  stage 
of  school  instruction.  Failing  in  this  respect,  many 
teachers  are  often  found  most  laboriously  occupied  in 
the  useless  task  of  attempting  to  do  that  for  the  child 
which  nature,  without  any  assistance,  has  already  ac- 
complished. They  do  not  seem  to  be  aware  of  the  ex- 
tent to  which  the  pupil's  mental  faculties,  more  especi- 
ally these  concerned  in  observation,  have  been  developed 
in  this  way.  The  acquisitions  made  by  a  child  of  four 
or  five  years  of  age,  before  being  placed  under  any  regu- 
lar tuition  at  all,  or  subjected  to  any  of  the  manipula- 
tions of  the  school  teacher,  are  indeed  wonderful.  The 
senses,  actively  awake,  have  brought  the  young  mind 
into  communication  with  the  multifarious  objects  of 
external  nature;  the  faculty  of  conception,  peculiarly 
active  in  childhood,  has  given  it  a  number  of  ideas  cor- 
responding to  its  perceptions,  and  the  faculty  of  speech 
has  enabled  i£  to  connect  with  thousands  of  these  ideas, 
words  and  combinations  of  words,  so  as  to  designate  and 
express  them. 

Thus  is  the  foundation  of  the  intellectual  character 
unerringly  laid  by  the  unaided  operation  of  nature  her- 
self. Here  is  no  senseless  cramming  of  words,  for 
words  are  only  learned  after  the  ideas  which  they  repre- 
sent have  been  acquired.  Under  the  guidance  of  a 
teacher  properly  conversant  with  the  iaws  of  the  mind 


INTRODUCTION.  13 

and  its  growth,  this  natural  process  would  be  continued, 
and  would  be  directed  to  its  proper  objects ;  but,  instead 
of  this,  a  mental  treadmill  is  often  used,  the  effect  of 
which  is  to  counteract  the  work  of  nature,  and  check 
the  mental  activity  of  the  young  pupil.  To  learn 
A,  B,  C  is,  of  course,  necessary  as  one  of  the  rudimen- 
tal  steps  of  primary  instruction  ;  but  this,  like  every- 
thing else,  should  be  so  done,  that  the  intelligence  of 
the  pupil  may  be  fostered,  not  deadened,  in  the  acquisi- 
tion. In  every  stage  of  intellectual  training,  let  the 
teacher  always  remember,  that  his  pupil's  mind  is  not 
to  be  treated  as  a  "passive  recipient  "  of  the  thoughts 
and  experience  of  others,  but  as  an  active  agent,  to  be 
enabled  to  acquire  an  experience  of  its  own,  and  apply  it 
to  useful  purposes.  Let  him  constan  tly  apply  the  princi- 
ple, so  tersely  expressed  b,y  Sir  William  Hamilton  :  "  Tlie 
primary  principle  of  education  is  the  determination  of  the 
pupil  to  self -activity— the  doing  nothing  for  him  which  he 
is  able  to  do  for  himself."  This  principle  is  equally  ap- 
plicable to  every  stage  of  the  mind's  development,  as 
well  as  to  the  different  processes  of  instruction  adapted 
to  these  stages ;  but  it  will  be  impossible  accurately 
and  effectively  to  apply  it,  without  a  complete  knowl- 
edge of  the  order  of  mental  development,  and  of  the  re- 
lation of  that  development  to  the  study  of  each  of  the 
branches  prescribed  for  the  instruction  and  the  cultiva- 
tion of  the  miiid. 

Knowledge  is  to  be  considered  as  the  food  of  the 
mind;  since  by  the  proper  reception,  digestion,  and 
assimilation  of  it,  the  mind  is  to  attain  a  maturity  of 
strength  and  efficiency;  and  upon  its  quality  and  quan- 
tify it  must  depend  whether  that  mind  is  to  be  healthy 
and  vigorous,  or  puny,  sickly,  and  imbecile.  It  is, 
therefore,  of  the  greatest  importance  to  ascertain  the 


14  INTRODUCTION. 

effect  produced  upon  the  mind  of  the  pupil  by  the 
study  of  each  separate  branch  of  knowledge — what 
faculties  it  exercises  and  develops,  and  what  it  keeps  in 
a  state  of  abeyance  or  passiveness.  The  future  wants  of 
the  pupils  as  to  information,  must,  indeed,  be  a  promi- 
nent consideration  in  selecting  the  subjects  to  be  taught ; 
but  the  teacher  should,  in  the  classification,  as  well  as 
the  instruction,  of  his  pupils  constantly  keep  in  view  the 
present  status  of  their  minds — what  they  especially  need 
in  order  to  acquire  vigor,  promptitude,  and  efficiency  of 
action.  In  the  first  stages  of  education,  the  latter 
should  be  the  almost  exclusive  consideration  ;  but  as 
education  advances,  the  practical  usefulness  of  the 
knowledge  imparted  should  have  paramount  weight  and 
importance. 

The  adaptation  of  the  processes  of  teaching  to  the 
various  subjects  taught,  as  well  as  to  the  faculties  which 
they  call  into  exercise,  should  be  a  prominent  object  in 
the  teacher's  mind.  Young,  untrained,  inexperienced 
teachers  commit  the  error  of  bringing  into  play,  with 
regard  to  all  subjects,  association  or  memory.  This, 
with  imitation,  enables  the  pupil  to  present  a  show  of 
knowledge,  very  gratifying  to  the  unintelligent  obser- 
ver, but  exceedingly  pernicious  as  a  substitute  for  real 
acquisitions.  When  a  teacher  conceives  that  the  sole 
end  of  his  efforts  is  to  enable  the  pupil  to  recite  verba- 
tim the  contents  of  a  particular  text-book,  or  to  repeat 
with  verbal  accuracy  and  fluency  certain  rules,  defini- 
tions, and  formulae,  whether  their  true  meaning  is 
grasped  or  not,  it  is  natural  that  he  should  resort  to  the 
shortest  and  most  direct  means  of  accomplishing  it,  that 
is,  constant  rote  drill — an  appeal  to  the  law  of  arbi- 
trary association.  The  injury,  however,  done  to  the 
mind  by  this  continued  process,  is  incalculable;  since. 


INTRODUCTION.  15 

finally,  ideas  and  facts  suggest  each  other  according  to 
no  intrinsic  or  philosophical  relation,  but  only  from 
their  accidental  connections,  or  such  as  this  constant 
repetition  may  have  established ;  and  thus  all  logical 
flow  of  thought  is  necessarily  precluded. 

A  determination  of  what  are  the  best  methods  of  pre- 
senting the  subjects  to  be  taught  must  depend  upon  the 
relations  here  referred  to.  Eules  and  methods  may,  in- 
deed, be  arbitrarily  learned  and  mechanically  applied  to 
practice,  without  any  investigation  of  principles,  but  no 
such  hap-hazard  process  can,  in  any  case,  be  sure  of 
success ;  while  in  very  many  it  must  result  in  failure. 
This  important  part  of  the  theory  of  teaching  should 
be  carefully  studied,  not  only  as  preliminary  to  entering 
upon  the  duties  of  an  instructor,  but  through  every 
stage  of  their  performance.  It  involves  not  only  a 
knowledge  of  the  laws  of  mind,  but  a  thorough  famil- 
iarity with  the  subjects  taught.  "A  teacher,"  says  Ed- 
ward Everett,  "ought  to  know  of  everything  much 
more  than  the  learner  can  be  expected  to  acquire.  The 
teacher  must  know  things  in  a  masterly  way,  curiously, 
nicely,  and  in  their  reasons.  He  must  see  the  truth 
under  all  its  aspects,  with  its  antecedents  and  conse- 
quents, or  he  cannot  present  it  in  just  that  shape  in 
which  the  young  mind  can  apprehend  it.  He  must, 
as  he  holds  the  diamond  up  to  the  sun,  turn  its  facets 
round  and  round,  till  the  pupil  catches  its  luster." 

A  very  important  inquiry  in  connection  with  the  right 
manner  of  presenting  the  subjects  to  the  pupils'  minds, 
is  in  what  manner  the  subjects  should  be  divided  into 
topics,  and  how  these  topics  should  be  arranged,  and  in 
what  order  they  should  be  taken  up.  The  following 
work,  embodying,  as  it  does,  a  graded  course  of  instruc- 
tion, is  designed  to  deal  with  this  inquiry  quite  exhaust- 


1 6  INTRO D  UCTION. 

ively,  and  it  is  in  furnishing  a  guide  to  the  teacher  in 
this  important  part  of  his  duties  that  its  usefulness  will 
be  found  to  consist. 

The  teacher  should  study,  too,  the  phenomena  of 
morbid  as  well  as  of  healthy  growth ;  for  teaching,  in 
the  complete  discharge  of  its  functions,  has  much  to  do 
in  reforming,  as  well  as  forming,  the  mind.  While  very 
much,  in  this  regard,  can  be  learned  only  by  experience, 
there  are  many  facts  and  principles  already  established, 
which  the  teacher  should,  as  an  essential  part  of  his 
professional  preparation,  acquire.  In  this  connection, 
the  automatic  tendencies  of  the  mind  are  to  be  studied — 
the  tendencies,  that  is,  to  fall  into  habits,  these  when 
depraved  constituting  what  may  be  called  the  morbid 
growth  of  the  mind.  No  part  of  the  teacher's  duty  is 
more  important  than  the  exercise  of  a  constant  vigi- 
lance, in  order  to  arrest  the  formation  of  deleterious 
habits,  or  to  aid  in  forming  such  as  are  calculated  to 
confirm  the  healthy  progress  and  development  of  the 
pupil's  mind.  It  is  on  this  account  that  teachers  are 
constantly  to  be  reminded  that  habits  are  always  more 
valuable  than  facts  —  that  it  is  not  the  quantity  of 
knowledge  acquired  that  constitutes  a  criterion  of  men- 
tal advancement,  but  the  mode  of  employing  the  men- 
tal faculties — the  habits  of  thought  into  which  the  mind 
has  settled  in  making  its  acquisitions  or  in  applying 
them.  In  such  useful  arts  as  require  a  mixed  exercise 
of  the  muscular  system  and  the  mental  faculties,  such 
as  penmanship,  drawing,  elocution,  etc.,  this  automatic 
tendency  has  a  most  important  application.  Elegant 
hand-writing,  distinctness  of  articulation,  correctness 
of  intonation,  ease  and  grace  of  deportment,  may  all  be 
made  to  rest  so  firmly  on  thoroughly  fixed  habits  as  to 
become  a  kind  of  "second  nature." 


INT  ROD  UCTION.  1 7 

How  to  use  text-looks,  as  well  as  when  and  for  what 
purposes  to  employ  them,  is  at  the  present  time  particu- 
larly, a  most  important  subject  of  study  to  the  teacher. 
Though  in  some  branches,  and  for  the  attainment  of 
certain  objects  of  mental  discipline,  it  is  best  to  dispense 
with  them  altogether  and  bring  the  mind  of  the  teacher 
in  direct  contact  with  that  of  the  pupil,  yet  good  text- 
books must  always  be  among  the  most  important  instru- 
mentalities of  school  instruction,  both  as  regards  the 
effect  which  their  judicious  use  has  upon  the  mind  of 
the  pupil,  and  the  economy  of  time  and  labor  of  which 
it  is  the  source  to  the  teacher.  The  latter  must  have 
learned  how  to  use  them  aright  in  order  to  be  successful 
in  his  work,  and  the  pupil  must  learn  how  to  make  ef- 
fective use  of  books  to  be  truly  educated. 

Most  children  enter  school  for  the  first  time  with 
minds  athirst  for  knowledge.  They  have  received  this 
craving  at  the  hands  of  Nature,  and  their  whole  existence 
has  been  passed  in  the  effort  to  satisfy  it.  By  their  own 
unaided  intelligence  they  are  able  to  proceed  to  a  certain 
limited  extent ;  observation  is  on  the  alert,  and  reflection 
begins  to  be  active ;  but  without  the  guidance  of  a  ma- 
ture and  trained  intellect,  there  can  be  no  method  in 
their  acquisitions,  and  the  limit  of  their  researches  is 
soon  reached.  The  teacher  and  the  book  are  the  instru- 
ments for  affording  this  necessary  aid  and  direction ;  but 
in  doing  this,  the  tendency  should  always  be  to  stimu- 
late, not  repress,  intellectual  activity — to  bring  into 
play  the  higher  faculties  of  the  mind,  not  to  render  its 
energies  dormant  by  offering  only  the  dry  forms,  the 
mouldy  skeletons  of  knowledge,  instead  of  the  vital 
germs  of  intelligence  and  thought.  If,  after  the  various 
grades  of  school  study  have  been  passed,  the  pupil  is 
left  with  a  torpid,  vacant  mind,  the  loss  which  he  has 


18  INTRODUCTION. 

sustained  is  too  great  to  be  compensated  by  even  the 
ability  to  read,  write,  and  cipher.  On  the  other  hand, 
a  pupil  that  has  not  only  mastered  the  elementary  prin- 
ciples of  science,  but  has  learned  how  to  use  books  so 
as  to  supplement  the  result  of  his  own  observations  by 
the  experience  of  others,  has  been  more  eifectually  edu- 
cated than  he  could  possibly  be  by  an  exclusive  depend- 
ence upon  oral  instruction. 

One  of  the  most  serious  abuses  to  which  the  employ- 
ment of  elementary  text-books  is  liable,  is  the  practice 
of  requiring  the  pupil  to  commit  to  memory,  verbatim, 
all  the  definitions  of  a  subject  before  teaching  the  subject 
itself,  so  as  to  enable  the  pupils  to  understand  the  nature 
of  the  things  defined.  It  is,  of  course,  most  logical  in 
the  scientific  treatment  of  a  subject  to  place  the  defini- 
tions first,  and  the  reasoning  based  upon  them  afterward, 
but  this  is  not  the  order  of  investigation.  The  defini- 
tions are  the  results  of  an  induction  based  upon  the 
facts  obtained  by  observation  ;  they  are  generalizations 
of  those  facts,  and  are  unintelligible  to  those  entirely 
unacquainted  with  the  facts  themselves.  Thus  the  order 
of  investigation  is  inductive ;  the  treatment  is  deductive, 
and  in  elementary  teaching  the  method  should  conform 
rather  to  the  former  than  the  latter.  Give  the  pupil 
accurate  and  vivid  conceptions  of  the  facts,  encourage 
him  to  observe  the  phenomena — to  collect  an  experience 
of  his  own ;  tell  him,  or  let  him  learn  from  the  book 
what  has  been  discovered  by  the  experience  of  others ; 
and  when  the  facts  thus  obtained  form  a  sufficient 
ground-work,  lead  his  mind  to  the  proper  induction, 
after  which  the  definition,  principle,  or  rule,  based  upon 
it,  comes  naturally,  and  will  be  thoroughly  under- 
stood. The  definitions  thus  taught  should  be  brief  and 
accurate  in  language,  and,  as  a  general  thing,  should  be 


INTRODUCTION.  19 

committed  to  memory  verbatim  ;  for  great  skill  is  re- 
quired to  construct  a  good  definition,  and  it  is  of  the 
greatest  value  to  the  scholar  and  thinker  to  have  his 
mind  well  stored  with  these  landmarks  and  guide-posts 
of  knowledge. 

There  is  a  numerous  class  of  subjects  in  which  text- 
books, in  the  hands  of  the  pupil,  are  apt  to  be  a  bane 
rather  than  a  benefit.  The  general  recognition  of  this 
fact  is  quite  an  interesting  feature  in  the  educational 
history  of  our  times.  Object  Teaching  and  Oral  In- 
struction have  assumed  a  prominent  place  in  every  ra- 
tional course  of  study.  Both  these  terms  necessarily 
exclude  the  use  of  text-books.  Teaching  from  objects 
is  merely  training  the  young  child  to  acquire  knowledge, 
in  a  systematic  way,  from  his  own  experience;  that  is, 
by  the  regular  exercise  of  his  observing  faculties.  It 
presupposes  the  presentation  of  the  actual  object  during 
the  early  stages  of  the  work,  so  that  perceptions  may 
pass  from  it  to  the  mind,  and  thus  ideas  be  obtained. 
In  teaching  natural  science,  at  an  advanced  stage  of  the 
course,  the  same  method  is  needed;  for  it  is  of  very 
little  nse  to  attempt  to  teach  facts  in  relation  to  the 
phenomena  of  nature  when  those  phenomena  have  never 
been  observed.  It  is  of  no  use  to  talk  of  the  laws  of 
light,  heat,  and  electricity — of  the  movements  and  ap- 
pearances of  the  heavenly  bodies — or  of  the  chemical 
composition  of  ordinary  substances,  as  if  they  were  mere 
abstractions.  The  teacher  should  never  forget  that  the 
study  of  the  book  is  the  instrument,  not  the  end  of  in- 
struction ;  its  lifeless  representatives  of  ideas  cannot 
dispense  with  those  vivid  expressions  of  thought  which 
come  fresh  from  the  lips  of  the  teacher.  Besides,  there 
is  a  language  other  than  words — a  language  to  which 
the  eye,  the  tones  of  the  voice,  the  movements  of  the 


20  INTRODUCTION. 

body,  all  give  force  and  expressiveness,  and  added  to 
these  there  is  the  influence  of  sympathy,  which,  though 
a  kind  of  "  unconscious  tuition,"  is  perhaps  the  greatest 
element  of  the  teacher's  power;  and  this  not  alone,  or 
chiefly,  in  intellectual  training,  but  in  that  which  is  far 
more  important — moral  education.  The  government 
of  his  pupils — the  training  of  their  sensibilities,  their 
emotional  nature,  and  their  impulses — the  instilling  of 
right  principles  of  conduct  —  all  these  constitute  a 
greater  part  of  what  may  be  called  a  good  education, 
than  the  teaching  of  the  rudiments  of  knowledge. 
"  Give  me  the  child,"  says  Everett,  "  whose  heart  has 
embraced  without  violence  the  gentle  lore  of  obedience, 
in  whom  the  sprightliness  of  youth  has  not  encroached 
on  deference  for  authority,  and  I  would  rather  have  him 
for  my  son,  though  at  the  age  of  twelve  he  should  have 
his  alphabet  to  learn,  than  be  compelled  to  struggle 
with  the  caprice  of  a  self-willed,  obstinate  youth,  whose 
bosom  has  become  a  viper's  nest  of  unamiable  passions, 
although  in  early  attainments  he  maybe  the  wonder  of 
the  day." 


GRADED  COURSE  OF  INSTRUCTION. 


TEI^TH     GRADE. 

(LOWEST   PRIMARY.) 
Time  allowed,  about  Jive  months. 

LANGUAGE. 

Reading. — Words,  and  what  they  represent ;  their  sounds, 
and  letters  ;  also  short  sentences  composed  of  familiar  words. 
The  alphabet,  by  review. 

Phonetics. — Simple  sounds  of  letters  for  training  the  organs 
of  hearing  and  of  speech. 

Spelling.— Words  of  regular  formation — to  be  taught  from 
the  blackboard,  charts,  etc. 

ARITHMETIC. 

Counting  and  Adding* — Objects — as  balls  on  the  Nu- 
meral Frame,  pebbles,  etc. 

Figures.— From  0  to  100,  as  symbols  of  the  numbers,  taught 
by  counting  objects. 

OBJECT  LESSONS. 

Form. — Common  shapes,  as  square,  oblong,  ball,  cylinder, 
cube ;  different  kinds  of  corners,  and  of  lines. 


22  GRADED  COURSE  OF  INSTRUCTION. 

Color, — Common  colors,  as  red,  yellow,  blue,  green,  orahge, 
purple,  to  be  distinguished. 

Objects. — Names  of  common  objects,  their  uses,  and  principal 
parts. 

Human  Body. — Principal  parts  of  the  body. 

DRAWING  AND  WRITING. 

On  Slates* — Making  dots  and  small  crosses  in  rows ;  draw- 
ing short  lines,  corners,  etc.    Printing  or  writing  simple  letters. 

MANAGEMENT. 
Length  of  Exercises. — Fifteen  minutes  at  one  time. 

Discipline. — Constant,   but  varied  employment  the  best 
means. 


LANGUAGE.  23 

How  TO  TEACH 

SUBJECTS  OF  TIIE  TENTH  (OR  LOWEST  PRIMARY)  GRADE. 


LANGUAGE. 

Reading. — Children  learn  words  as  audible  signs 
or  names  of  objects,  actions,  and  qualities,  Avhen  they 
begin  to  talk.  These  words  are  learned  as  wholes,  at 
once,  by  hearing  them  spoken ;  not  by  first  learning 
their  elementary  sounds.  In  this  manner  young  chil- 
dren gradually  become  familiar  with  new  words  until 
they  possess  a  vocabulary  which  enables  them  to  make 
known  their  wants,  and  to  express  their  thoughts.  The 
words  which  the  children  thus  learn  make  but  little 
impression  upon  their  minds,  as  words,  but  they  are  so 
intimately  associated  with  the  objects,  actions,  and 
qualities  which  they  represent  that  they  convey  to  the 
mind  the  same  ideas  as  the  objects  or  the  actions  them- 
selves convey. 

When  a  child  first  goes  to  school  it  has  already  learned 
many  words,  by  hearing,  as  symbols  of  objects,  etc.  The 
first  duty  of  the  teacher  is,  to  ascertain  what  words  the 
child  thus  knows,  then  to  teach  the  young  pupil  to 
recognize  them  by  their  forms.  The  spoken  words  are 
first  learned  as  wholes;  the  printed  words  should  be 
learned  first  as  wholes  and  associated  with  both  the 
spoken  words  and  the  objects  which  they  represent. 

Therefore,  teach  first  short  words,  which  the  children 
have  learned  by  hearing;  beginning  with  the  names  of 
familiar  objects  which  can  be  shown  to  the  pupils,  or 
the  pictures  of  which  may  be  presented.  Also,  during 


24  HOW  TO  TEACH 

the  first  lesson  in  reading,  print  the  Avords  on  the  black- 
board several  times,  and  point  them  out  on  charts,  etc. 
Let  the  pupils  point  out  the  words  on  the  blackboard, 
and  on  charts ;  also  let  them  print  the  words  on  their 
slates. 

Special  pains  should  be  taken  to  lead  the  children  to 
associate  the  printed  words  with  the  objects  which  they 
-represent,  either  by  the  use  of  the  objects  themselves, 
or  by  pictures. 

In  teaching  words  that  are  not  names,  care  should  be 
taken  to  illustrate  their  meaning  by  simple  phrases, 
conversations,  etc.  During  the  earlier  lessons,  omit 
words  of  irregular  formation,  having  several  silent  let- 
ters, such  as  tongue,  knife,  know,  though,  thought,  etc. 
This  class  of  words  may  be  presented  when  the  pupils 
have  learned  the  alphabet,  and  its  regular  combinations, 
and  the  sounds  represented  by  the  letters  have  been 
taught. 

Let  each  word  be  taught  first  at  sight,  as  a  whole, 
and  the  sounds  and  names  of  the  letters  which  com- 
pose the  word  be  taught  afterward.  After  the  chil- 
dren have  learned  a  few  words  at  sight,  they  may  be 
taught  the  sounds,  and  the  letters  Avhich  form  those 
Avords.  For  the  purpose  of  teaching  the  sound-elements 
of  Avords,  select  those  in  Avhich  the  sounds  and  letters 
are  similar,  as  cat,  rat,  hat,  mat,  ox,  fox,  box,  etc.  The 
teacher  should  sound  the  elements  or  letters  of  the 
words  first,  then  require  the  pupils  to  imitate  the 
sounds  thus  made.  But  before  this  can  be  done  suc- 
cessfully the  pupils  must  be  trained  to  distinguish,  and 
to  produce  these  sounds,  as  directed  under  the  head  of 
Phonetics  for  this  grade,  Avhich  see.  As  additional 
Avords  are  learned,  the  children  may  be  required  to 
name  such  of  the  letters  as  they  knoAV,  in  the  new 


LANGUAGE.  25 

words,  and  then  taught  the  remaining  onos  in  those 
words.  In  this  way  let  the  twenty-six  letters  of  the 
alphabet  be  taught,  progressively.  Subsequently  these 
should  be  reviewed,  and  their  usual  order  learned  by 
repetition.  The  small  letters  are,  of  course,  to  be 
taught  first. 

After  the  pupils  have  learned  several  single  words, 
simple  sentences  may  be  presented,  as  "  The  dog  can 
bark."  "  The  horse  can  draw  a  cart."  The  other 
words  that  make  up  these  sentences  can  then  be 
learned  easily,  as  parts  of  the  sentence. 

The  rapidity  with  which  a  child  may  be  taught  to 
read  by  learning  to  recognize  the  simple  forms  of 
words,  at  first,  is  surprising.  And  no  less  astonishing 
is  the  readiness  with  which  spelling  is  afterward 
learned. 

Let  the  order  of  teaching  reading  be, first,  the  idea; 
then,  its  sound- symbol,  or  spoken  word  ;  next,  the  form- 
symbol,  or  printed  word ;  and  subsequently,  its  represen- 
tation by  writing ;  and  the  order  of  learning  to  read 
the  language  will  correspond  with  the  order  of  using  it. 
Words,  then,  will  become  as  mirrors,  reflecting  ob- 
jects and  ideas  to  the  minds  of  the  pupils.  Sense,  and 
found,  and  form,  and  use  will  become  so  intimately 
blended  together  that  pupils  may  easily  be  led  to  use 
"conversational  tones  in  reading,  and  a  natural  style  of 
expression  will  follow  as  the  necessary  result. 

But  it  may  be  asked,  How  can  the  pupils  acquire 
the  means  of  learning  the  new  words  which  they  will 
find  in  reading  ?  By  observing  their  resemblances  to 
words  already  learned.  The  child,  while  learning  to 
read,  is  constantly  comparing  the  forms  of  new  words 
with  the  forms  and  sounds  of  those  previously  mas- 
tered. The  teacher  may  and  should  aid  the  young  pup;  U« 


26  HOW  TO  TEACH 

in  acquiring  the  ability  to  learn  new  words  by  arranging 
in  groups,  on  the  blackboard,  those  already  learned, 
and  showing  them  how  to  compare  the  forms  and 
sounds  of  these  words  with  others. 

For  the  purpose  of  leading  the  children  to  observe 
readily  the  analogy  of  words,  in  their  sounds  and  in 
the  arrangement  of  their  letters,  after  they  have 
learned',  objectively  and  singly,  to  recognize  several 
words  at  sight,  place  on  the  blackboard,  in  columns, 
such  of  these  words  as  are  similar  in  spelling  and  in 
sound,  as  in  the  following  groups: 


cat, 

pin, 

pen, 

ox, 

ctip, 

rat, 

tin, 

hen, 

fox, 

(jun, 

hat, 

fin, 

ten, 

box, 

run, 

mat. 

in. 

men. 

top. 

fun. 

When  the  children  have  learned  to  pronounce  the 
words  in  a  column,  at  sight,  let  them  learn  to  give  the 
sounds  of  each,  as — k&t,  cat;  r&t,  rat;  hdt,  hat; 
etc.,  not  as  a  spelling  exercise,  but  to  impress  upon  their 
minds  the  relation  of  sounds,  and  of  letters  as  their 
representatives. 

As  other  words  are  learned,  let  new  groups  be  arranged, 
and  comparisons  made  with  words  of  similar  form,  as: 

old,  rake,  me,  line,  mule, 

cold,  make,  we,  fine,  rule, 

told,  cake,  see,  nine,  cube, 

scold.  bake.  bee.  pine.  tube. 

Familiar  Words. — The  list  of  familiar  words 
taught  in  this  grade  should  include  those  commonly  used 
as  names  of  articles  of  food,  dress,  furniture,  utensils 
used  in  the  house,  in  the  garden,  or  on  the  farm,  and 


LANGUAGE.  27 

different  articles  used  in  the  school-room,  also  names 
of  common  animals,  familiar  qualities,  actions,  etc., 
such  as,  bread,  fish,  cap,  vest,  chair,  bed,  etc. 

Phonetics. — The  object  of  teaching  this  subject 
should  \)Q,first^to  train  the  organs  of  hearing,  so  that 
the  children  may  readily  distinguish  the  sounds  heard 
in  speaking  our  language  ;  second — to  train  the  organs 
of 'speech,  so  that  the  pupils  may  learn  to  produce  those 
sounds  correctly  in  using  the  language.  In  presenting 
this  subject — and  this  should  be  done  as  soon  as  the 
children  begin  to  learn  words  by  sight — the  teacher 
should  herself  make  the  sounds,  and  then  require  the 
pupils  to  imitate  them,  as :  a,  a ;  &,  d ;  0,0;  0,6;  e,e; 
e,8;  1,1',  1,1;  u,u;  -&,&;  a,  a',  a,  a ;  afterward,  thus : 
a,  d,d,a;  e,8;  1,1;  0,0,0;  u,  ti,  u. 

When  their  organs  of  hearing  and  of  speech  have  thus 
been  trained,  both  to  distinguish  and  to  imitate  sounds, 
proceed  to  teach  what  sounds  are  represented  by  the 
letters  of  simple  words,  as — m  e,  mat ,  cat ,  man, 
no,  not,  pin,  cup,  met,  cake,  make,  late, 
slate. 

Should  more  definite  directions  relative  to  methods 
for  giving  the  first  lessons  in  Phonetics  be  desired  for 
this  and  the  following  grades,  see  pages  297-308  in 
Neio  Primary  Object  Lessons,  by  N.  A.  Calkins. 

Spelling. — After  the  words  have  been  learned  by 
sight  and  sound,  let  them  be  learned  by  spelling,  and 
the  children  requested  to  observe  that  similar  spelling 
and  similar  sounds  usually  accompany  each  other.  Of 
course  many  words  must  be  taught  simply  as  signs  of 
things,  or  actions,  or  qualities,  etc.,  but  the  plan  of 
grouping  words  by  similarity  of  sounds,  as  indicated 


28  HOW  TO  TEACH 

on  a  preceding  page,  under  the  head  of  Reading,  will 
greatly  facilitate  learning  to  read,  and  to  spell,  also. 

Various  modes  may  be  used  in  teaching  the  reading 
and  the  spelling  of  words  singly — for  instance:  Let  the 
pupil  point  out  given  words  on  the  blackboard,  and  on 
the  charts,  as  they  are  named  by  the  teacher.  A  word 
may  be  erased  from  the  blackboard,  and  the  pupils  re- 
quested to  pronounce  the  word,  and  name  the  letters 
composing  it.  Parts  of  words  may  also  be  erased,  and 
the  pupils  required  to  name  the  missing  letters.  Let 
the  pupils,  also,  print  the  words  on  slates,  copying  them 
from  charts,  or  the  blackboard. 

The  list  of  familiar  words  taught  during  the  first 
term  in  school  should  include  those  commonly  used,  as, 
names  of  articles  of  dress,  food,  furniture,  and  utensils 
used  in  the  house,  different  things  used  in  the  school- 
room, common  animals,  plants,  names  of  familiar  quali- 
ties, actions,  etc. 

It  is  not  the  small  number  of  letters  of  which  a  word 
is  formed  that  renders  it  easy  to  be  learned  objectively, 
but  its  familiarity  by  use  in  conversation.  Do  not,  there- 
fore, confine  the  pupils  to  words  which  are  composed  of 
only  three  or  four  letters.  Long,  difficult,  or  anomalous 
words  should,  however,  be  omitted  in  this  grade.  . 

N.  B. — In  all  these  exercises  of  reading  and  spelling, 
the  teacher  should — 

Train  the  pupils  to  pronounce  ivords  readily  at  sight. 

Never  allow  them  to  use  unnatural  tones  in  speaking 
or  reading. 

Correct  their  faults  in  the  use  of  language  as  they 
occur. 


ARITHMETIC. 


ARITHMETIC. 

Counting  and  Adding. — The  child's  knowl- 
edge of  number  commences  with  counting  objects.  He 
cannot  learn  the  value  of  figures  from  1  to  10  until  he 
can  count  ten  objects.  Therefore  counting  should  be 
attended  to  first.  The  Numeral  Frame  is  the  most 
convenient  apparatus  to  aid  in  teaching  counting,  and 
in  giving  children  first  ideas  of  simple  numbers.  The 
following  illustration  is  intended  to  represent  one  mode 
of  using  the  Numeral  Frame  for  teaching  counting. 
This  mode  of  using  it  consists  simply  in  holding  the 
Frame  before  the  pu- 
pils, and  moving  the 
balls  on  the  first  wire, 
one  at  a  time,  while 
the  children  count 
"  one,  two,  three,  four, 
five,  six,  seven,  eight, 
nine,  ten."  The  same 
counting  may  be  re- 
peated on  the  second, 
third,  and  on  each 
succeeding  wire.  At 
first  the  counting 
should  not  extend  be-  COUNTING. 

yond  ten.  When  all  the 

balls  on  each  wire  have  been  counted  in  this  manner, 
proceed  to  move  one  ball  on  each  wire,  and  let  the  chil- 
dren count  to  ten,  as  before.  Let  this  exercise  be  con- 
tinued, from  day  to  day,  until  each  child  can  count 
from  one  to  ten,  alone.  Afterward,  the  counting  may  be 
extended  to  twenty,  by  moving  the  balls  on  two  wires ; 
then  to  thirty,  by  moving  the  balls  on  three  wires,  and 


30  HOW  TO  TEACH 

"o  on  to  one  hundred.  When  the  pupils  are  allowed  to 
count  in  concert,  care  should  be  taken  to  have  them 
use  the  falling  inflection  at  each  number,  to  prevent 
them  from  acquiring  a  sing-song  tone. 

Adding* — When  the  pupils  can  count  to  one  hun- 
dred by  ones,  the  teacher  may  move  two  balls  at  a  time, 
and  thus  train  them  to  add  by  twos.  As  the  teacher 
moves  two  balls  on  one  wire,  and  two  more  on  the  next, 
and  so  on,  the  pupils  say,  "  two,  four,  six,  eight,  ten, 
twelve,  fourteen,"  etc. 

After  the  pupils  can  count,  or  add  thus  by  twos,  as 
far  as  fifty,  and  have  also  learned  to  read  and  write  fig- 
ures as  far  as  20,  the  teacher  may  write  a  column  of  2's 
on  the  blackboard,  and  train  the  pupils  to  add  the  fig- 
ures in  the  same  manner  as  the  balls  were  added. 

Next,  the  pupils  may  copy  the  column  of  2's  from 
the  blackboard,  on  their  slates,  and  each  one  add  it  as 
it  was  added  on  the  blackboard,  and  write  the  sum 
under  the  column. 

When  the  pupils  have  had  sufficient  practice  on  a 
column  of  2's,  both  on  the  blackboard  and  on  their 
slates,  to  be  able  to  add  it  readily,  the  teacher  may  again 
take  the  Numeral  Frame,  move  one  ball  on  the  first 
wire,  and  two  balls  on  each  succeeding  wire,  while  the 
pupils  say,  "one,  three,  five,  seven,  nine,  eleven,"  etc., 
to  fifty-one.  When  the  pupils  have  learned  to  add  the 
balls,  thus,  the  teacher  may  write  a  column  of  2's  with 
a  1  under  it,  on  the  blackboard,  so  as  to  make  the 
combinations  produce  the  odd  numbers.  After  suffi- 
cient training  upon  these  combinations,  both  with  the 
Numeral  Frame,  and  the  blackboard,  require  the  pupils 
to  write  similar  columns  of  2's  with  a  1  underneath, 
and  add  as  before,  writing  the  sum  below  the  column. 


-  ARITHMETIC.  31 

Let  the  same  process  be  pursued  in  teaching  the  ad* 
dition  of  threes  ;  first,  by  balls  on  the  Numeral  Frame, 
as  three,  six,  nine,  twelve,  etc.,  then  by  figure  3's  oil 
the  blackboard,  and  lastly  by  each  pupil's  writing  the 
figures  in  columns  on  the  slate,  adding  them,  and 
writing  the  sum  below.  Then  the  threes  should  be 
combined  with  one,  next  with  two,  so  as  to  produce  dif- 
ferent combinations  of  numbers,  as  with  the  twos. 

During  a  still  later  stage,  the  pupils  may  be  taught 
to  add  by  alternating  twos  and  ones;  then  threes  and 
ones ;  then  threes  and  twos ;  then  threes,  twos,  and 
ones.  Each  of  these  steps  should  be  taken  first  with 
objects,  then  with  figures  on  the  blackboard,  and  finally 
by  the  pupils'  writing  the  columns  on  their  slates  and 
adding  them.  The  same  method  may  be  pursued  for 
teaching  the  addition  of  fours,  fives,  and  sixes,  and 
their  combinations  with  ones,  twos,  threes,  etc.,  in  the 
next  or  Ninth  Grade.  The  order  of  the  steps  is  indi- 
cated by  the  objects  employed  in  teaching,  viz.:  Num- 
eral Frame,  Blackboard,  Slates. 

Of  course,  these  exercises  with  columns  of  figures 
should  not  be  introduced  before  the  pupils  have  been 
taught  to  know  figures  as  symbols,  and  to  make  them 
on  their  slates. 

Value  of  Numbers. — It  is  exceedingly  impor- 
tant that  the  first  ideas  of  the  value  of  numbers,  and  of 
figures,  be  associated  with  numbers  of  objects  counted. 
Both  the  value  of  numbers  and  the  value  of  figures 
should  be  taught  in  connection  with  counting  objects. 
Here,  again,  the  Numeral  Frame  is  the  most  useful  ap- 
paratus. When  the  pupils  can  readily  count  ten,  the 
teacher  may  hold  the  Numeral  Frame  before  the  class, 
move  one  ball  on  the  second  wire  from  the  top,  and 


110 W  TO  TEACII 


request  the  pupils  to  say  "one  ball."  Then  the  teacher 
may  move  two  balls,  one  at  a  time,  on  the  third  wire, 
the  pupils  counting  them  as  moved,  thus:  "one,  two; 
two  balls."  Then  move  three  balls,  one  at  a  time,  on 
the  fourth  wire,  the  pupils  counting  thus:  "one,  two, 
three  ;  three  balls."  Then  move  four  balls  in  the  same 
manner ;  then  five  balls,  and  so  011.  The  position  of 
the  balls  on  the  wire  while  the  pupils  are  counting, 
may  be  seen  on  the  sixth  wire  in  the  accompanying 

illustration  of  the 
Value  of  Numbers. 
While  the  pupils 
are  counting  "one, 
two,  three,  four, 
five,"  the  teacher 
does  not  move  the 
balls  to  the  side 
of  the  frame,  but 
leaves  a  space  be- 
tween each  two 
balls,  as  may  be  seen 
in  the  illustration 
on  this  page. 

The  illustration 
on  the  next  page 
— Simple  Value  of 
Figures— represents 

the  teacher  in  the  act  of  moving  ihefive  balls  to  the  side 
of  the  frame ;  and,  as-  he  does  this,  the  pupils  tell  the 
number  of  balls,  thus,  "  five  balls."  Let  the  same  mode 
be  pursued  with  each  number,  from  one  to  nine.  First, 
the  children  count  the  separated  balls,  as  each  is  moved 
part  way;  and  as  all  are  moved  to  the  side  of  the 
frame,  the  pupils  tell  the  whole  number  of  balls  moved. 


VALUE  op  NUMBERS. 


ARITHMETIC. 


Next  let  the  pupils  tell  the  number  of  balls  on  each 
wire,  thus:  one  ball,  two  balls,  three  balls,  four  balls, 
five  balls,  six  balls,  etc.,  to  nine  balls ;  nine  balls,  eight 
balls,  seven  balls,  etc.,  to  one  ball,  no  ball.  By  these 
means  the  Value  of  Numbers  will  be  learned  thoroughly. 

Fif/ures. — Figures  should  be  introduced  as  sym- 
bols of  the  number  of  objects  counted,  and  presented 
first  consecutively,  in  groups,  or  steps,  as  follows:  from 
0  to  9;  from  10  to  19 ;  from  20  to  29;  from  30  to  39, 
etc.  No  succeed- 
ing group  should 
be  presented  unt'.l 
the  preceding  one 
has  been  thorough- 
ly learned,  so  that 
the  pupils  can  read 
them  at  sight,  in 
order,  and  out  of 
order.  While  teach- 
ing the  Simple 
Value  of  Figures, 
the  Numeral  Frame 
will  be  found  a 
most  valuable  aid. 

During    this     Stage  SIMPLE  VALUE  OF  FIGURES. 

of  instruction   the 

teacher  should  make  frequent   use  of  the  blackboard, 

and  the  pupils  of  slates. 

Additional  suggestions  relative  to  methods  for  teach- 
ing the  First  Ideas  of  Numbers  and  of  Figures,  may  be 
found  on  pages  194-209  of  New  Primary  Object  Lessons. 

2* 


34  HO  W  TO  TEACH 


OBJECT  LESSONS. 

N.  B. — Each  exercise  in  object  lessons  should  be  con- 
ducted with  a  vieiv  to  .forming  habits  of  attention  and 
careful  observation  through  the  use  of  the  senses. 

Form. — In  Nature's  school,  children  first  learn  to 
know  things  as  wholes ;  they  learn  to  know  their  parts 
afterward.  The  teacher  who  would  be  successful  must 
follow  Nature's  plan  of  instruction.  Present,  therefore, 
common  objects,  as  wholes,  and  lead  the  pupils  to  notice 
resemblances  in  shape,  first;  afterward  direct  their  at- 
tention to  prominent  differences. 

A  Box  of  Forms  and  Solids,  containing  forty-eight 
plane  Forms  and  fifteen  Solids,  has  been  prepared  for 
the  special  purpose  of  Object  Teaching.  This  is  the 
most  important  aid  in  illustrating  the  various  forms 
and  solids. 

Select  the  Form  to  be  taught  from  the  Box  of  Forms, 
and  lead  the  pupils  to  observe  it,  then  tell  them  its 
name;  next  require  them  to  mention  other  objects 
having  the  same  shape.  Proceed  in  this  manner  with 
each  Form  and  Solid  mentioned  for  this  grade,  and 
continue  these  exercises  until  the  pupils  can  recognize 
and  name  each. 

Color. — The  pupils  should  be  led  to  distinguish  re- 
semblances and  differences  in  color  from  "  colored 
cubes,"  or  cards,  and  to  group  together  objects  of  like 
colors.  They  should  also  learn  the  names  of  the  six 
principal  colors. 


DRAWING  AND   WRITING.  35 

Objects. — The  lessons  on  Common  Objects  in  this 
grade  should  be  simple  and  conversational,  treating 
only  of  their  most  obvious  parts  and  uses.  Such  com- 
mon objects  as  a  bell,  chair,  slate,  pencil,  hat,  cup,  knife, 
etc.,  are  appropriate  for  this  purpose.  The  pupils  should 
be  led  to  notice  and  point  out  the  principal  parts,  and 
encouraged  to  tell  what  they  see  and  what  they  know 
of  each  object  shown  them. 

Human  JZody. — In  this  Grade  the  lessons  on  the 
Human  Body  should  lead  the  pupils  to  notice  and  name 
the  parts,  as  head,  neck,  trunk,  arms,  hands,  legs,  feet; 
also  parts  of  the  head,  as  crown,  face,  forehead,  cheeks, 
chin,  mouth,  nose,  eyes,  ears,  etc.  . 

N.  B. — If  more  explicit  information  be  desired  rela- 
tive to  methods  for  giving  lessons  on  shapes  of  lines, 
corners,  square,  oblong,  ball,  cylinder,  cube,  and  common 
objects  ;  also  on  colors,  and  on  the  human  body,  it  may 
be  found  in  Neiv  Primary  Object  Lessons. 


DRAWING  AND  WRITING. 

Drawing  on  Slates,  etc. — The  exercises  of 
Drawing  and  Printing  on  slates  should  be  introduced 
in  such  a  manner  as  to  give  an  interesting  variety  to 
the  class-work;  also,  so  as  to  aid  in  the  discipline  of 
the  class,  by  giving  the  children  something  to  do  that 
will  interest  them  after  they  have  become  tired  with 
their  other  lessons.  The  children  might  be  allowed  io 
use  slates  for  drawing,  as  a  reward  for  good  order  and 
attention.  Short  daily  exercises  may  be  made  very 
useful. 


36  HOW  TO  TEAVH 


MANAGEMENT. 

Length  of  Exercises. — The  exercises  of  this 
Grade  should  not  be  continued  upon  the  same  subject 
longer  than  fifteen  minutes  at  one  time,  without  mate- 
rially changing  the  manner  of  the  exercise. 

Discipline. — Young  children  cannot  attend  to 
the  same  thing  for  a  long  time  without  change  in  the 
form  of  attention.  Their  natural  activity  demands  fre- 
quent changes  in  the  position  of  the  body;  also  con- 
stant but  varied  employment.  If  the  teacher  does  not 
furnish  the  needed  employment  and  changes  of  position 
by  variety  in  her  methods  of  instruction,  the  children 
will  seek  to  gratify  their  needs  by  play.  Therefore  chil- 
dren should  never  be  compelled  10  sic  without  employ- 
ment, cither  for  the  mind,  the  hands,  or  the  body. 

Children  should  be  led  to  do  right  by  encouragement 
rather  than  driven  by  fear.  Judicious  praise  is  more 
efficient  than  scolding.  Teach  them  to  be  cleanly, 
mannerly,  truthful,  and  obedient.  Let  good  examples 
of  these  traits  be  commended  frequently. 


NINTH    GRADE. 

(PR1MAKY.) 

Time  allowed,  about  five  months. 


LANGUAGE. 

Reading. — In  the  First  Reader. 

Phonetics. — Pupils  to  be  taught  to  recognize  and  to  make 
the  sounds  of  the  letters  in  words  of  one  syllable. 

Definitions. — Pupils  to  be  practiced  in  illustrating  the  mean- 
ing of  words  by  their  use  in  short  sentences;  also  in  telling  what 
the  words  mean. 

Spelling. — Words  from  the  reading  lessons;  also  familial 
words  in  common  use. 

ARITHMETIC. 

Adding.— With  objects,  and  with  figures;  twos,  threes,  fours, 
and  fives. 

Figures. — Numbers  of  two  and  of  three  figures  to  be  read  at 
sight,  without  numeration ;  also,  to  be  written  on  slates  from 
dictation. 

Roman  Numbers. — I,  V,  X,  L.  with  their  combinations 
to  sixty,  inclusive  ;  also  their  use  on  the  face  of  the  clock. 

OBJECT  LESSONS. 

Form. — Common  shapes,  continued ;  adding  ianse  of  rhomb, 
rhomboid,  circle,  semicircle,  crescent,  sphere,  hemisphere,  cone; 
also  position  of  lines. 


38  GRADED  COURSE  OF  INSTRUCTION. 

Color. — Shades  of  common  colors,  as  light  and  dark  red, 
light  and  dark  blue,  etc. 

Human  Body. — Names  and  uses  of  the  limbs,  and  of  their 
parts ;  also  the  names  and  shapes  of  the  principal  bones. 

Objects. — The  principal  parts  and  chief  uses  of  common 
objects. 

DRAWING  AND  WRITING. 

On  Slates. — Connect  dots  by  lines ;  draw  squares,  oblongs, 
rhombs  ;  divide  lines  into  equal  parts.  Write  simple  words  with 
small  letters. 


MANAGEMENT. 

Doing. — Train  children  to  see,  to  do,  and  to  tell. 

Manners  and  Morals.— Use  the  appropriate  daily  inci- 
dents of  school  as  occasions  for  giving  instruction  in  Manners 
and  Morals. 


LANGUAGE. 


39 


LANGUAGE. 

Reading. — The  manner  of  teaching  Reading  dur- 
ing the  first  term  in  which  books  are  used  by  the  pupils, 
has  a  very  important  influence  on  the  future  progress 
of  those  pupils.  In  the  processes  of  instruction,  only 
one  difficulty  should  be  presented  to  the  pupils  at  a 
time.  Among  the  difficulties  which*  children  have  to 
encounter  during  their  first  lessons  in  reading  from 
books,  are,  learning  to  know  the  words  at  sight,  so  as  to 
pronounce  them  readily ;  learning  to  know  what  the 
words  and  sentences  mean;  learning  to  read  in  such  a 
manner  as  to  imitate  good  conversation. 

First  Step. — With  each  new  reading  lesson  the  first 
step  should  be  to  make  the  pupils  familiar  with  the 
words  of  the  lesson,  by  printing  them  on  the  blackboard 
in  columns,  and  teaching  the  children  to  pronounce 
them  at  sight ;  next  teach  them  to  pronounce  at  sight 
the  same  words  in  the  book,  but  out  of  their  order  in 
the  sentences  of  the  lesson,  lest  they  learn  them  by  rote, 
instead  of  by  sight. 

Second  Step. — Train  the  pupils  to  find  out  what  each 
sentence  means,  and  to  tell  the  meaning  in  their  own 
language. 

Third  Step. — Train  the  pupils  to  read  each  sentence 
so  that  the  reading  may  resemble  good  conversation. 


40  HOW  TO  TEACH 

Finally,  when  the  lesson  has  been  read  in  a  proper  man- 
ner, the  teacher  should  talk  with  the  children  about  it, 
and  encourage  them  to  tell,  in  their  own  language,  what 
they  have  read. 

N.  B. — Let  the  standard  for  good  reading  be  its  near 
resemblance  in  manner  to  good  conversation. 

Further  suggestions  relative  to  first  lessons  in  read- 
ing from  books  may  be  found  on  pages  333-337,  of  New 
Primary  Object  Lessons. 

***  The  work  of  teaching  children  to  read  may  be  facilitated 
by  using,  for  the  First  and  Second  Reading  Books,  those  printed 
with  the  modified  types  invented  by  Dn.  EDWIN  LEIGH. 

Phonetics. — The  object  of  exercises  in  Phonetics 
should  be  the  same  in  this  grade  as  in  the  preceding — 
to  secure  a  ready  recognition  of  the  several  sounds  of 
our  language,  and  the  ability  to  utter  them  distinctly  in 
conversation  and  reading.  Time  should  not  be  wasted 
in  the  endeavor  to  teach  children  definitions  or  descrip- 
tions of  the  various  sounds  of  letters. 

Let  the  chief  aims  of  the  teacher  be,  to  train  the 
organs  of  hearing  to  acuteness  in  the  perception  of 
sounds,  and  the  organs  of  speech  to  flexibility  and  accu- 
racy in  producing  sounds. 

Definitions. — During  the  lessons  of  this  grade,  it 
is  appropriate  to  teach  the  children  to  use  the  principal 
words  of  the  lesson  in  brief  sentences,  to  enable  them 
to  show  readily  that  they  understand  what  the  Avords 
mean,  as :  "A  horse  can  draw  a  cart" — "  I  must  be 
good" — "I  can  hold  a  book." — "Snow  is  white." — "I 
will  try  to  learn  to  read." — "I  must  obey  my  mother," 


ARITHMETIC.  41 

etc.,  etc.  Such  exercises  will  be  found  to  be  much 
more  useful  to  young  children  than  teaching  them 
formal  definitions  to  be  recited.  The  meaning  of  diffi- 
cult or  unusual  words  must,  of  course,  be  explained  and 
illustrated  by  the  teacher. 

Spelling. — In  oral  spelling,  the  words  should  be 
distinctly  pronounced  by  the  pupil  before  they  are 
spelled,  then  each  letter  clearly  uttered,  a  pause  made 
between  the  syllables,  and  the  word  again  pronounced 
after  all  the  letters  have  been  given.  The  familiar 
words  taught,  in  addition  to  those  in  the  reading  les- 
sons, should  include  such  appropriate  words  as  the 
children  most  commonly  hear  and  use.  These  should 
be  printed  or  written  on  the  blackboard  by  the  teacher, 
and  copied  by  the  pupils,  on  their  slates.  The  same 
words  may  also  be  spelled  orally. 

The  chief  use  of  spelling  consists  in  writing  words; 
therefore,  as  early  as  possible,  it  should  be  taught  by 
writing.  As  the  first  step  in  this  direction,  let  pupils 
commence  in  this  grade  to  study  spdliny  lessons  ly 
copying  the  words  on  slates. 


ARITHMETIC. 

Adding. — It  would  be  well  for  the  teacher,  before 
commencing  the  lessons  of  this  Grade,  in  Arithmetic, 
to  read  the  directions  for  teaching  "  Adding "  in  the 
preceding  Grade. 

During  the  exercises  of  counting  and  adding  Avith 
the  Numeral  Frame,  do  not  allow  the  children  to  count 
and  add  by  rote.  See  that  due  attention  is  given  to 
the  objects  counted.  When  the  pupils  can  add  readily 


42  HOW  TO  TEACH 

single  columns,  each  composed  of  like  numbers,  as  all 

2's,  all  3's,  4's,  o's,  etc.,  teach  them  to  add  single  columns 

composed  of  different  small  numbers,  as  2's  and  3's; 

2's,  3's,  and  4's ;  also  2's,  3's,  4's,  and  5's. 

245     These  combinations  should  be  illustrated 

3        3        4    on  the  Numeral  Frame  at  first,  then 

223     taught  with  figures  on  the  blackboard ; 

342    and  subsequently  copied  by  the  pupils  on 

2  3         5     their  slates,  and  added  by  them  silently. 

3  2        4    In  adding,  let  the  pupils  be  trained  from 
243     the  first  to  name  only  the  sums,  thus: 
3         3         2     3,  5,  8,  10,  13,  15,  18,  20,  23,  25  ;— 4,  G, 
2259,  13,  15,  18,  22,  24,  27,  31 ;— 4,  9,  11, 
3        4        4     14,  18,  23,  25,  28,  32,  37. 

To  make  the  pupils  familiar  with  the 
25      31       37     sums  produced  by  adding  the  separate 
numbers,    1,  2,  3,   4,   5,  6,  7,  8,  9,  to 
each  number  below  20,  arrange  the  figures  on  the  black- 
board thus: 

012345678      9    10     11     12     13    14    15       etc. 
111111111      1      1      1       1       1      1      1 

1     2    3    4    5    G    7    8    9    10     11     12     13     14     15    16 


01234567      8      9     10     11     12     13    14    15 
2222222222222222 

2    3     4    5     G     7     8     9     10     11     12     13     14     15     16     17 


Continue  this  arrangement  until  the  pupils  can  add, 
both  on  the  blackboard  and  on  slates,  each  number 
from  1  to  9  to  each  number  below  20,  both  in  the  order 
given,  and  out  of  this  order. 


ARITHMETIC.  43 

Heading  and  Writing  Figures. — Both  the 
reading  and  writing  of  numbers  in  figures  can  be 
taught  most  thoroughly  in  steps,  or  groups.  The 
figures  should  be  presented  first  in  their  order,  in  con- 
nection with  counting ;  then  out  of  their  order.  In 
this  Grade  the  figures  should  be  taught  without  nume- 
ration. The  following  groups  will  indicate  appropriate 
steps : 

First  Step.     Second  Step.    TJiird  Step.   Fourth  Step.    Fifth  Step. 

10  100  100  200  300 

11  200  101  201  301 

12  300  102  202  302 

13  400  103  203  303 

14  500  104  204  304 

15  600  105  205  305 

16  700  106  206  306 

17  800  107  207  307 

18  900.  108  208  308 

19  109  209  309 

20  110  210  310 

21  111  211  311 
etc.,  etc.,  etc.,  etc., 
to  to  to  to 
99.  199.  299.  399. 

These  steps  may  be  continued  in  tli  is  manner  through 
999.  As  much  time  will  be  required  to  teach  the  first 
and  third  steps  as  for  any  four  other  steps.  Let  the 
children  be  trained  to  read  and  write  the  numbers  con- 
tained in  each  step,  readily,  before  taking  up  the  next 
one  in  order. 

If  properly  conducted,  these  lessons  will  train  the 
pupils  to  read  and  write  numbers  through  199  in  one 
month,  and  any  number  expressed  by  three  figures  in 
two  months. 


HOW  TO  TEACH 


Roman  Numbers.  —  Besides  teaching  what  num- 
bers are  represented  by  I,  V,  X,  and  L,  and  their  com- 
binations to  sixty,  the  pupils  should  be  trained  to  tell 
the  time  of  day  as  indicated  on  the  face  of  a  clock. 


OBJECT  LESSONS. 

Form* — When  the  pupils  have  learned  to  recognize 
a  given  shape  by  means  of  its  representative  form  in 
the  set  of  "  Object  Teaching  Forms  and  Solids,"  they 
should  be  led  to  discover  the  same  shape  in  several 
other  objects.  See  remarks  on  page  34,  relative  to 
Form  and  Methods  for  teaching  it. 

During  the  first  lessons  on  lines,  the  attention  of  the 
pupils  was  properly  directed  to  their  shapes  only,  as 
straight,'  crooked,  curved,  waved,  spiral.  When  they 
are  taught  to  recognize  and  name  the  positions  of  lines, 
as  vertical,  slanting  or  oblique,  and  horizontal,  they 
should  be  trained  to  apply  these  names  of  positions  to 
objects  as  well  as  to  lines. 

Color. — In  lessons  on  color,  the  name  should  first 
be  associated  with  the  color  which  it  represents,  by 
showing  that  color  and  requiring  the  pupils  to  point 
it  out  on  the  chart,  and  among  colored  objects.  To 
recite  names  and  descriptions  of  colors,  without  also 
knowing  the  color  when  seen,  is  of  no  use.  The  teacher 
should  use  "Color-Cubes,"  "Colored-Cards,"  "Color- 
Charts,"  and  other  colored  objects  for  illustrating  these 
lessons,  and  require  the  pupils  to  show,  by  placing  in 
groups  colors  that  nearly  resemble  each  other,  with 
what  degree  of  accuracy  they  distinguish  colors;  and 
at  the  same  time  they  should  be  taught  to  know  com- 
mon shades  and  tints  by  their  names. 


DRAWING  AND  WRITING.  45 

Human  Body. — In  giving  the  lessons  on  the 
human  body,  let  the  pupils  point  out  and  give  the 
names  and  uses  of  parts,  as  parts  and  uses  of  the  arm, 
hand,  leg,  foot,  etc. 

Objects. — Let  the  pupils  point  out  parts  of  objects, 
and  the  teacher  give  their  names  and  uses ;  then  let  the 
children  give  the  names  and  uses  of  the  parts  as  the 
teacher  points  to  them. 

N.  B. — Should  the  teacher  desire  more  explicit  in- 
formation relative  to  methods  for  giving  lessons  on 
plane  forms,  solids,  position  of  lines,  shades  of  colors, 
the  human  body,  and  on  common  objects,  for  this  and 
the  succeeding  Grades,  than  the  space  will  allow  in  this 
book,  it  may  be  found  in  the  treatment  of  these  topics 
in  New  Primary  Object  Lessons. 

DRAWING  AND  WRITING. 

On  Slates. — In  this  Grade,  the  instruction  should 
be  continued  in  a  manner  similar  to  that  for  the  Tenth 
Grade,  which  see.  The  teacher  should  give  full  illus- 
trations on  the  blackboard,  relative  to  each  point  and 
step  of  the  lessons. 

MANAGEMENT. 

Doing. — Children  learn  much  faster  by  doing  than 
by  merely  repeating  what  they  have  been  told.  There- 
fore, whenever  possible,  arrange  the  exercises  of  each 
subject  so  that  the  pupils  may  be  called  upon  to  do 
something  which  relates  to  that  subject,  with  their 
hands ;  also  so  as  to  require  them  to  tell  what  they  see 
and  do. 


46  JIOW  TO  TEACH. 

Regular  Occupation  for  all  the  Pupils.— 

A  teacher  who  furnishes  that  regular  and  constant  oc- 
cupation which  commands  the  attention  of  all  the  pu- 
pils during  the  several  exercises  of  the  day,  thereby 
gives  the  best  assurance  of  ability  to  manage  a  school 
successfully.  Indeed,  the  secret  of  maintaining  good 
discipline  chiefly  lies  in  this.  Hence  the  manner  of 
teaching  becomes  an  important  element  of  good  man- 
agement as  well  as  of  good  instruction,  for  it  is  this 
which  chiefly  determines  the  order  of  the  class.  Fur- 
thermore, habits  of  learning  are  acquired  from  the  pre- 
vailing methods  of  teaching. 

To  learn  how  to  manage  a  class  or  school,  so  that  all 
the  pupils  may  have  constant  occupation,  and  may  give  an 
interested  attention  to  all  the  exercises,  should  be  the 
aim  of  every  teacher.  Proper  changes  in  the  manner 
of  presenting  the  different  lessons  upon  the  same  subject, 
and  even  changes  in  the  manner  of  conducting  the  ex- 
ercise of  a  single  lesson  will  be  useful  to  the  teacher 
toward  the  attainment  of  this  aim. 

In  a  class  composed  of  young  children,  frequent  alter- 
nations from  answers  by  individual  pupils  to  responses 
by  the  entire  class  will  aid  in  maintaining  the  attention 
of  all  the  pupils.  Great  care,  however,  will  be  necessary, 
on  the  part  of  the  teacher,  to  prevent  the  pupils,  while 
speaking  in  concert,  from  using  sing-song  tones.  This 
may  be  prevented  by  requiring  them  always  to  use  the 
falling  inflection  in  answers  by  the  entire  class,  and  by 
never  allowing  them  to  repeat  the  answer,  or  statement, 
without  a  request  from  the  teacher,  made  after  each  re- 
sponse by  the  class. 


EIGHTH    GKADB. 

(PRIMARY.) 
Time  allowed, — about  five  months. 


LANGUAGE. 

Heading. — First  Reader  completed,  and  an  easy  Second 
Header  commenced ;  pupils  to  be  able  to  read  fluently  in  good 
conversational  tones,  with  proper  attention  to  the  pauses. 

Phonetics. — Sounds  occurring  in  words  of  one  syllable,  and 
silent  letters  to  be  distinguished. 

Definitions. — Meaning  of  the  words  read  to  be  shown  by 
using  them  in  short  sentences. 

Spelling. — From  reading  lessons  ;  and  lists  of  other  familiar 
words. 

ARITHMETIC. 

Adding. — Single  columns  of  ten  figures  ;  adding  by  decades, 
through  9s'. 

Numeration  and  Notation. — Heading  and  writing  figures 
through  nine  places  (987,  654,  321). 

Mental. — Simple,  practical  questions  which  require  the  add- 
ing of  numbers  from  5  to  9  to  numbers  below  30 ;  also,  subtract- 
ing similar  numbers. 

Multiplication  table  commenced. 

Roman  Numbers. — Their  combinations  through  two  hun- 
dreds. The  Key  to  Roman  Numbers  to  be  taught. 


48  GRADED  COURSE  OF  INSTRUCTION. 


OBJECT  LESSONS. 

Form. —  Parallel  and  perpendicular  lines,  angles,  prism*, 
pyramids,  surfaces,  circumference,  diameter,  etc. 

Color. — Primary  and  secondary  colors. 
Human  Body.— Principal  bones  and  their  uses. 

Animals, — Names  and  uses  of  familiar  an-imals  ;  also  where 
they  live. 

Plants. — Names  of  trees,  plants,  flowers,  fruits,  etc. ;  also 
where  they  grow. 

Objects. — Principal  qualities,  parts,  and  uses. 


DRAWING  AND  WRITING. 

On  Slates. — Drawing  plaue  figures  ;  writing  simple  words  , 
formation  of  capitals  taught. 

MANAGEMENT. 

Physical  Training.— Daily  physical  exercise  and  pure 
air  are  indispensable  to  the  health  of  children.  Provide  them 
with  both  during  the  hours  of  school  duties. 


LANGUAGE.  49 

How  TO  TEACH 

SUBJECTS    OF  THE   EIGHTH   GRADE. 


LANGUAGE. 

. — The  exercises  for  teaching  Reading  in 
the  Eighth  Grade  may  be  divided  into  three  steps,  as  in 
the  Ninth  Grade. 

First  Step. — Training  the  pupils  to  know  the  words 
at  sight ;  also  what  the  words  mean. 

Second  Step. — Attention  to  the  thoughts  expressed. 
Third  Step. — Eeading  in  easy,  conversational  tones. 

1.  The  pnpils  may  be  trained  to  know  the  words  at 
sight  by  writing  them  in  columns  on  the  blackboard — 
by  pronouncing   them  from  their  books,  commencing 
with  the  last  word  of  the  paragraph  and  proceeding  in 
an  order  the  reverse  of  that  pursued  in  reading. 

2.  As  soon  as  the  words  are  known  readily  at  sight, 
chief  attention  should  be  given  to  the  thoughts  expressed. 
The  pupils  may  be  led  to  attend  to  the  thoughts  ex- 
pressed by  requiring  them  to  find  out  what  the  senten- 
ces tell,  without  reading  them  aloud.     The  teacher  may 
aid  them  in  this  matter  by  proceeding  in  a  manner 
similar  to  the  following:   Request  the  class  to  look  at 
the  first  sentence,  and  each  member  to  raise  a  hand  when 
able  to  tell  what  the  sentence  is  about.     When  several 
hands  are  held  up,  call  upon  different  pnpils  to  state,  in 
their  own  language,  what  the  sentence  tells.     Proceed  in 
a  similar  manner  with  other  sentences  of  the  lesson,  and 

3 


50  HOW  TO  TEACH 

require  the  pupils  to  tell  what  those  sentences  say.  The 
teacher  may  ask :  What  does  the  first  line  tell  us  ? 
What  do"  the  words  in  the  next  sentence  say  ?  Who  can 
tell  what  the  next  paragraph  is  about  ? 

3.  When  the  pupils  have  accomplished  the  first  two 
steps  in  a  given  reading  lesson,  they  will  be  prepared  to 
take  the  third  step,  and  will  readily  learn  to  read  with 
easy,  conversational  tones.  Special  care  should  be  taken 
in  this  grade  to  train  the  pupils  in  habits  of  clearness 
and  distinctness  of  enunciation,  also  to  read  in  an  easy, 
speaking  voice. 

Faults  in  reading  are  most  readily  overcome  when  the 
efforts  to  correct  them  are  chiefly  directed  to  one  kind 
at  a  time,  and  the  training  continued  until  the  pupils 
clearly  perceive  the  fault  and  take  the  proper  means  to 
correct  it. 

Punctuation. — The  time  commonly  spent  in  teach- 
ing children  to  recite  definitions  of  punctuation-marks 
is  wasted.  Instead  of  this,  lead  the  pupils  to  observe 
that  a  short  pause  is  made  at  a  comma,  a  little  longer 
pause  at  a  semicolon,  and  still  longer  pauses  at  the 
question-mark  and  period.  Lead  the  pupils  to  see  that 
the  question-mark  points  out  a  question,  and  a  period 
the  end  of  a  sentence.  The  uses  of  all  the  marks  of 
pauses,  as  well  as  the  hyphen,  apostrophe,  and  quota- 
tion-marks, should  first  be  explained  from  the  black- 
board, then  examples  of  their  use  should  be  pointed 
out  by  the  pupils  in  their  reading  books. 

Phonetics* — In  this  grade  the  pupils  should  be 
taught  to  distinguish  the  sounds  of  given  letters  in 
words  of  one  syllable,  and  to  make  these  sounds,  as,  the 
sound  of  a  in  slate,  a  in  ball,  o  in  not,  o  in  do,  u  \\\  full, 


LANGUAGE.  51 

fin  far,  fin  of,  k  in  kite,  m  in  man,  c  in  cow,  etc. 
When  the  pupils  can  distinguish  and  make  the  sounds 
in  words  of  one  syllable,  they  may  be  required  to  tell 
which  letters  have  no  sound  in  given  words ;  also,  to 
name  the  vowel  sound  by  its  number ;  as  in  the  word 
make,  m-a-k,  make,  a  has  its  first  sound,  the  e  is  silent ; 
bought,  b-a-t,  bought ;  ou  represents  the  fourth  sound  of 
a,  g  and  h  are  silent. 

As  a  method  for  training  pupils  to  distinguish  the 
silent  letters,  let  them  first  sound  a  word,  giving  each 
sound  as  heard  when  the  word  is  properly  pronounced 
— then  spell  it,  naming  each  letter  in  order — next  tell 
which  letters  have  no  sound. 

Care  needs  to  be  taken,  in  each  grade,  to  prevent  the 
pupils  from  making  the  short  sounds  of  a,  e,  i,  o,  and  u, 
too  long,  when  sounded  alone.  Let  each  of  these 
sounds  be  made  very  short,  as  heard  in  at,  net,  it,  not, 
nut. 

Definitions* — In  giving  the  meaning  of  separate 
words,  in  some  instances  a  description  of  the  object,  or 
of  its  use,  if  the  word  be  a  name,  or  a  simple  statement 
about  that  which  is  meant  by  it,  will  illustrate  the 
pupil's  understanding  of  it  better  than  the  use  of  the 
word  in  a  sentence.  Let  this  exercise  be  so  conducted 
as  to  avoid  mechanical  forms  of  definition,  and  with  a 
sufficient  variety  and  simplicity  to  secure  a  clear  knowl- 
edge of  the  meaning  of  the  words.  The  practice  of 
using  the  given  words  in  sentences,  so  as  to  illustrate 
their  meaning,  should  be  continued  in  this  grade. 

Spelling. — Care  should  be  taken  in  oral  spelling  to 
have  each  pupil  pronounce  the  word  before  spelling  it, 
to  name  each  letter  distinctly,  to  make  a  pause  between 


62  HOW  TO  TEACH 

the  syllables,  and  to  pronounce  the  word  again  when  all 
the  letters  have  been  named. 

As  soon  as  the  pupils  can  write  words  on  their  slater 
they  should  have  much  practice  in  spelling  by  writing 
words  from  dictation. 

In  selecting  familiar  words  it  would  be  well  to  re- 
quest the  pupils  to  name  words  for  the  teacher  to  write 
on  the  blackboard,  and  all  the  class,  afterward,  to  copy 
these  on  their  slates.  But  teachers  should  not  depend 
entirely  upon  the  pupils  for  such  words ;  they  should  add 
to  the  list  other  appropriate  common  words. 


ARITHMETIC. 

ing. — Continue  the  exercise  of  adding  single 
columns,  in  the  same  manner  as  in  the  Ninth  Grade, 

making  them  more 

66778899  difficult,  gradually, 
65768798  until  the  pupils  can 
64758697  add  readily,  without 
63748596  counting,  columns 
6  6  7  3  8  4  9  9  of  ten  or  twelve 
65778898  figures  each,  which 
6476879  7  are  composed  of 
6  3  7  5  8  6  9  6  7s,  8s,  and  9s. 
(5  6  7  4  8  5  9  9  The  progressive  ar- 
65738498  rangement  of  these 
64778897  columns  is  illus- 
63768796  trated  here.  When 
—  —  —  the  pupils  have 
learned  to  add  a 

column  on  the  blackboard,  they  should  copy  it  on  their 
slates,  and  then  each  add  it  singly,  writing  the  sum 
underneath  it. 


ARITHMETIC.  53 

Adding  by  Decades  will  greatly  facilitate  learning  to 
add  accurately  and  rapidly. 

Appropriate  steps  toward  teaching  pupils  to  add  by 
decades  may  be  taken  by  writing  various  combinations 
of  numbers  on  the  blackboard,  in  the  following  form 
and  order,  and  requiring  the  pupils  to  add  the  numbers 
orally,  and  afterward  to  copy  them  on  their  slates  and 
add  them  again : 

5       15      25      35       45       55       Co       75       85       95 
4444444444 

9       19       29       39       49       59       etc. 

7       17       27      37      47       57       07       77      87      97 

7777777777 

14       24      34       44       54       04       etc. 

9       19       29       39       49       59       09       79       89       99 

7777777777 

10       20       30       40       etc. 

When  the  various  combinations  with  each  of  the  nine 
digits  have  been  made  thus  in  the  form  of  decades,  the 
pupils  may  be  required  to  review  them  by  writing  on 
their  slates,  in  groups,  combinations  of  two  numbers 
each,  that,  when  added,  will  produce  in  the  unit  figures 
the  following:  0,  1,  2,  3,  4,  5,  0,  7,  8,  9. 

By  means  of  these  and  similar  exercises,  children 
can  be  led  to  observe  that  the  same  numbers  always 
produce  a  like  figure  when  added,  as  that  9  and  7 
always  give  the  unit  6,  whether  the  numbers  be  19 
and  7,  or  29  and  7,  or  37  and  9,  or  87  and  9 ;  and  thus, 
by  attending  to  this  fact,  while  adding  single  columns, 
they  can  readily  acquire  the  habit  of  adding  without 
counting.  One  of  the  most  effectual  means  toward  se- 
curing this  habit,  in  addition  to  the  adding  by  decades, 


54  JIOW  TO  TEACH 

is  to  teach  the  pupils  to  give  special  attention  to  the 
figure  representing  the  units  as  each  successive  number 
is  added,  i.  e.,  attention  to  adding  the  units. 

To  explain  this  process,  the  teacher  may  write  a  col- 
umn of  figures  on  the  blackboard,  as  represented  here 

a.       b.   by  the  one  marked  a.   Then  the  pupils  may  be 

7  —  0    led  to  notice  the  unit  figure  in  each  case  by 

8  —  3    the  teacher's  pointing  to  the  successive  num- 

9  —  5     bers  to  be  added,  and  saying:  "8   and    9 

6  —        will  give  7  for  the  unit  figure ;  7  and  5  will 

8  —  0    give  2  ;  2  and  9  will  give  1 ;  1  and  9  a  0 ;  5 

7  —  2    and  7  will  give  2 ;  2  and  8  a  0 ;  6  and  9  a  5 ; 
5  —        5  and  8  a  3 ;  3  and  7  a  0." 

9  —  0  During    this     explanatory    process,    the 
9  —  1  teacher  may  write  the  unit  figure  opposite 
5  —  2  the  number  added  which  produces  it,  as  rep- 
9  —  7  resented  in  the  column  marked  b.     So  soon 

8  —  as    the  pupils  understand  this  process  of 

adding  and  naming  the  unit  figures  only,  the 
90  teacher  should  erase  the  column,  b,  repre- 

senting these  units,  and  require  the  pupils  to  add  by 
naming  the  units,  as  follows :  8,  7,  2,  1,  0,  5,  2,  0,  6,  5, 
3,  0.  When  they  can  do  this  readily  from  the  black- 
board, the  pupils  may  copy  the  same  column  on  their 
slates,  and  add  by  naming  the  units  in  the  same  manner. 
Then  columns  made  up  of  other  figures  may  be  given 
for  similar  practice.  Afterward  the  pupils  may  be 
trained  to  add  by  naming  the  sum,  as  each  number  is 
added,  as  follows:  8,  17,  22,  31,  40,  45,  52,  60,  66,  75,  83, 
90.  This  last  form  should  be  followed  in  the  usual 
practice  of  addition.  The  preceding  ones  are  intended 
to  be  used  in  teaching  pupils  Jiow  to  add,  that  they  may 
acquire  correct  habits. 

Teachers  may  observe  that  the  number  of  figures  in 
the  column  marked  b,  corresponds  with  the  number  of 


ARITHMETIC.  55 

tens  in  the  sum  of  column  a  —  nine  —  and  that  9  tens, 
with  the  last  unit  figure,  0,  gives  the  sum  of  column  a. 
But  this  fact  is  not  of  sufficient  practical  importance  to 
render  it  desirable  that  much  prominence  should  be 
given  to  it. 

After  pupils  have  been  thoroughly  trained  in  adding 
single  columns,  and  understand  Numeration  and  Nota- 
tion, they  can  be  taught  the  process  of  "carrying"  in 
examples  of  two  or  more  columns,  by  a  few  lessons. 
For  teaching  the  pupils  "to  carry,"  at  first  the  examples 
should  be  very  short,  consisting  of  two  columns,  only. 
Afterward  the  examples  may  be  made  longer,  gradually, 
more  difficult  ones  being  given  by  extending  both  the 
length  of  the  lines  and  of  the  columns.  Give  many 
more  examples  with  a  few  long  columns  than  with  long 
lines.  Care  should  be  taken  not  to  embarrass  children  by 
giving  them  long  and  large  examples  in  addition  before 
they  can  readily  add  short  ones.  Let  the  training  be 
thorough  in  each  step,  and  the  progress  gradual.  The 
work  of  each  succeeding  week  ought  to  embrace  larger 
examples  than  were  given  during  the  previous  one,  and 
to  furnish  sufficient  practice  to  enable  the  pupils  to 
master  all  the  difficulties. 


*  —  On  commencing  Numeration,  the 
three  places  in  the  unit's  period  should  be  taught  by 
the  order  of  their  places,  and  by  their  names  ;  as,  unit's 
place,  the  first  place  on  the  right-hand  side;  ten's  place, 
the  second  place  from  the  right-hand  side;  hundred's 
place,  the  third  place  from  the  right-hand  side.  When 
the  pupils  can  name  each  place  at  sight,  both  in  order 
and  out  of  order,  from  the  blackboard,  and  can  write 
any  number  in  this  period  from  dictation,  proceed  to 
teach  the  thousand's  period  in  a  similar  manner.  The 
places  in  this  period  should  be  taught  first  as  the 


50  HOW  TO  TEA  OH 

fourth,  fifth,  and  sixth  places;  then  the  pupils  should 
be  led  to  observe  the  similarity  of  names  between  the 
first,  second,  and  third  places  of  the  unit's  period,  and  the 
first,  second,  and  third  places  of  the  thousand's  period; 
as  units,  tens,  hundreds  of  units  ;  units,  tens,  hundreds 
of  thousands.  When  the  pupils  can  both  read  and 
write  any  number  readily,  from  units  to  hundreds  of 
thousands,  proceed  in  the  same  manner  to  teach  the 
million's  period.  Train  the  pupils  so  that  they  can 
name  any  place  at  sight,  in  order  and  out  of  order,  and 
give  the  order  of  any  place  when  its  name  is  men- 
tioned ;  also  write  readily  any  number  through  hun- 
dreds of  millions,  from  dictation.  Care  should  be  taken 
to  teach  the  pupils  to  write  the  figures  neatly,  and  in 
straight  columns.  Two  or  three  weeks  may  be  spent  on 
the  unit's  period,  before  proceeding  to  the  thousand's 
period. 

Mental  Ariilimetic* — In  the  Eighth  Grade  the 
answers  to  the  questions  in  Mental  Arithmetic  should 
be  simple  and  concise.  The  language  used  should  be 
sufficient  to  render  the  solution  of  the  example,  and  the 
answer  to  it,  clearly  intelligible  to  a  listener,  yet  so  brief 
as  not  to  retard,  unnecessarily,  the  process  of  mental 
calculation.  Appropriate  forms  for  answering  questions 
in  Mental  Arithmetic,  in  the  Eighth  Grade,  may  be  seen 
in  the  following  examples: 

How  many  are  six  apples  and  three  apples  ? 
Ans. — Six  apples  and  three  apples  are  nine  apples. 

If  a  coat  cost  $15,  and  a  hat  $5,  how  much  will  both 
cost?  Ans. — Both  will  cost  the  sum  of  $15  and  $5, 
which  is  $20. 

Henry  had  8  marbles  and  bought  4  more  ;  how  many 
marbles  had  he  then  ?  Ans. — Henry  then  had  the  sum 
of  8  marbles  and  4  marbles,  which  is  13  marbles. 


ARITHMETIC.  57 

A  boy  had  9  apples  and  gave  away  5  of  them ;  how 
many  apples  had  he  left?  Ans. — He  had  4  apples  left; 
because,  when  5  apples  are  taken  from  9  apples,  4  apples 
will  remain. 

Multiplication  Table. — In  presenting  the  Mul- 
tiplication Table,  it  is  very  desirable  that  each  step  be 
thoroughly  mastered  before  taking  the  succeeding  one. 
This  table  may  be  illustrated  first  by  means  of  balls  on 
the  numeral  frame,  by  arranging  the  balls  in  groups  of 
twos,  then  of  threes.  When  the  groups  of  twos  have 
been  illustrated  by  the  balls,  the  teacher  may  write  the 
table  of  twos  on  the  blackboard,  thus : 


First  Form. 

Second  Form. 

First  Form. 

2  times  2  are  4 

3x2-   6 

2x3=  6 

3      "     2  "    G 

6x2  =  12 

3x3=  9 

4     "     2   "    8 

9x2  =  18 

4x3  =  12 

5     "     2   "10 

4x2=  8 

5x3=15 

6      «     2  "12 

7x2  =  14 

6x3  =  18 

7     "     2   "14,  etc. 

5x2  =  10,  etc. 

7x3=21,  etc. 

On  placing  the  Second  Form  before  the  class  for  tlje 
first  time,  the  teacher  should  explain  the  use  of  the 
signs  x  and  =.  The  pupils  may  be  told  to  read  the 
sign  of  multiplication  the  same  as  the  word  "  times," 
and  the  siyn  of  equality  the  same  as  "  are." 

Let  the  pupils  copy  and  learn  the  First  Form,  so  as 
to  repeat  it,  both  forward  and  backward.  Afterward 
place  the  Second  Form  on  the  blackboard,  and  let  the 
pupils  give  each  answer  orally  ;  also  copy  the  table  and 
write  the  answers.  When  the  table  of  twos  has  been 
learned  in  both  forms,  teach  the  table  of  threes  in  the 
First  Form,  then  in  the  Second  Form,  and  afterward 
review  both  of  them,  in  combination,  in  a  TJiird  Form, 
somewhat  as  follows : 


58  110  W  TO  TEACH 

Third  Form. 


4x2= 

8x3  = 

9x3  = 

4x3= 

5x3  = 

5x2= 

8x2  = 

6x3  = 

9x2= 

7x3  = 

2x6  = 

7x2= 

2x3  = 

6x2= 

3x4= 

3x9  = 

All  the  tables  may  be  taught  on  the  same  plan — first 
in  order,  then  out  of  order,  then  by  combination  with 
the  tables  previously  learned.  New  tables  should  not 
be  presented  before  the  pupils  have  learned  thoroughly 
each  preceding  one  through  the  three  forms. 

Roman  Numbers. — In  the  Eighth  Grade,  the 
Key  to  Roman  Numbers  should  be  explained  to  the 
pupils,  and  numerous  applications  of  it  made  to  a  vari- 
ety of  combinations,  viz.:  When  letters  representing 
equal  values  stand  side  by  side,  and  when  a  letter  rep- 
resenting a  smaller  number  stands  on  the  right-hand 
side  of  one  representing  a  larger  number,  the  values  of 
each  are  to  be  added,  as  II  two,  XX  twenty,  VI  six,  XV 
fifteen,  UK  sixty,  XXX  thirty.  When  the  letter  repre- 
senting a  smaller  number  stands  on  the  fr/V-hand  side 
of  one  representing  a  larger  number,  the  value  of  the 
Ze//Miand  letter  is  to  be  taken  from  the  value  of  the 
right-hand  letter,  as,  the  value  of  I  is  to  be  taken  from 
the  value  of  V  in  the  combination  IV,  which  gives 
four,  the  number  represented  by  IV;  the  value  of  X 
taken  from  the  value  of  L  in  XL  gives  forty  as  the 
number  represented  by  XL,  etc.  Training  the  pupils 
in  numerous  applications  of  this  Key  will  save  much  of 
the  time  usually  spent  in  memorizing  the  Roman  Num- 
bers. It  will  be  well  to  give  unusual  combinations, 
occasionally,  as— VL ;  VC;  VX;  VV;  XXXX;  LC; 
XLLV ;  etc.,  and  request  the  pupils  to  apply  the  Key 
and  tell  what  number  each  stands  for. 


OBJECT  LESSORS.  59 


OBJECT    LESSONS. 

Form. — Special  care  should  be  taken,  in  teaching 
various  Forms  and  Solids,  to  cause  the  pupils  to  dis- 
cover the  given  shape  in  other  objects  than  those  shown 
by  the  teacher  from  the  set  of  "  Object-Teaching  Forms." 
For  the  accomplishment  of  this  purpose  frequent  re- 
views should  be  had,  without  presenting  the  forms  which 
represent  the  shapes  that  have  already  been  learned, 
when  the  pupils  may  be  requested  to  mention  several 
objects  of  the  given  shapes. 

Lead  the  pupils  to  observe  that  all  prisms  have  oblong 
sides,  and  all  pyramids  triangular  sides;  that  prisms 
differ  in  the  number  of  their  sides,  and  in  the  shape  of 
their  ends;  that  pyramids  differ  in  the  number  of  their 
sides,  and  in  the  shape  of  their  bases. 

Lines  and  Angles. — In  teaching  pupils  what  consti- 
tutes parallel  lines,  lead  them  to  notice  the  fact  that  the 
lines  are  side-by-side  ;  that  they  are  the  same  distance 
apart  at  all  opposite  points  ;  afterward,  in  a  subsequent 
grade,  they  can  easily  be  led  to  observe  that  both  lines 
extend  in  the  same  direction  ;  also  that  they  can  never 
meet. 

In  previous  grades,  the  pupils  have  become  familiar 
with  the  terms  sharp,  square,  and  blunt,  as  applied  to 
corners;  use  this  knowledge  to  illustrate  the  different 
kinds  of  angles,  and  give  the  terms  acute,  right,  obtuse, 
to  be  applied  to  angles,  instead  of  sharp,  square,  and 
blunt.  In  explaining  the  terms  relative  to  lines,  angles, 
diameters,  etc.,  each  of  them  should  be  illustrated  on 
the  blackboard,  and  the  pupils  also  required  to  repre- 
sent them  on  their  slates. 


60  HOW  TO  TEACH 

Color. — All  the  lessons  on  Color  should  be  illus- 
trated with  "  Color-Charts,"  "  Color-Cubes,"  «  Colored 
Cards,"  pieces  of  ribbon,  silk,  worsted,  or  other  colored 
objects ;  also  with  good  water-colors.  Care  should  be 
taken  to  make  the  pupils  understand  that  by  mixing 
two  Primary  colors,  a  Secondary  color  will  be  produced ; 
also  that  no  Primary  color  can  be  formed  by  mixing  two 
Secondary  colors.  They  should  also  be  taught  which 
Primary  colors  will  produce  each  of  the  Secondary 
colors ;  and  what  two  Primary  colors  each  Secondary 
color  contains. 

If  desired,  more  definite  directions  relative  to  this 
matter  may  be  found  in  New  Primary  Object  Lessons. 

Human  Body. — It  is  important  that  the  pupils 
should  learn  to  point  out  the  location  of  those  bones 
and  other  parts  of  the  body  for  which  they  are  taught 
names  and  uses. 

Animals. — The  lessons  on  animals  should  at  first 
be  conversational,  and  of  such  a  character  as  to  lead 
the  children  to  notice,  when  away  from  school,  the 
various  kinds  of  movements  of  different  animals,  as, 
walking,  running,  jumping,  hopping,  flying,  swimming, 
etc. ;  so  that  they  may  be  able  to  tell  what  animals 
move  in  a  given  manner. 

After  the  teacher  has  led  the  children  to  observe  the 
different  classes  of  animals,  as  beasts,  birds,  fishes,  etc., 
by  showing  them  pictures  of  each,  let  them  be  requested 
to  give  the  names  of  some  animals  of  each  class  which 
they  have  seen.  The  names  thus  given  might  be  writ- 
ten on  the  blackboard  in  groups  corresponding  to  their 
several  classes. 

During  these  lessons  on  animals,  let  the  names  of 
those  used  for  food,  and  of  their  flesh,  be  written  on  the 


OBJECT  LESSONS.  61 

blackboard  as   the  children   mention  them,  and   the 
spelling  of  each  be  taught. 

Plants. — After  talking  with  the  children  about 
different  kinds  of  flowers,  plants,  grains,  fruits,  trees, 
etc.,  which  they  have  seen,  and  after  they  are  able  to 
name  several  of  those  most  common,  their  attention 
may  be  directed  to  different  parts  of  trees,  as,  roots, 
trunk,  branches,  limbs,  leaves,  etc.  The  teacher  will  find 
efficient  aid  in  presenting  this  subject,  by  the  use  of 
"  PKANG'S  Natural  History  Series,  for  Plants." 

Objects. — Pupils  should  be  led  to  point  out  and 
name  the  parts  of  common  objects,  to  tell  the  shape  of 
the  parts,  and  the  uses,  color,  etc.,  of  the  objects.  This 
exercise  should  be  so  conducted  as  to  give  the  children 
the  ability  to  describe  readily  objects  which  they  see. 

Objects  having  special  qualities  in  a  prominent 
degree  should  be  shown,  and  the  pupils  led  to  observe  a 
given  quality  in  several  objects,  as  a  means  of  teaching 
them  to  recognize  the  same  quality  whenever  it  may 
come  within  their  observation.  The  spelling  of  the 
words  representing  the  objects,  their  parts,  uses,  color, 
and  qualities,  may  be  taught. 

DRAWING  AND  WRITING. 

On  Slates. — All  necessary  explanations  and  illus- 
trations as  to  the  manner  of  drawing  figures,  the  forma- 
tion of  small  letters  and  capitals,  should  be  made  by  the 
teacher  from  the  blackboard,  first  to  the  whole  class ; 
afterward,  attention  may  be  directed  more  to  the  work 
of  individuals  of  the  class,  for  the  purpose  of  giving 
special  instruction. 


62  DRA  WING  AND    WHITING. 

Let  the  teacher  of  the  class  select,  each  day,  six  slates 
from  those  pupils  who  have  made  the  most  commend- 
able improvement  in  drawing  and  writing,  and  place 
them  on  her  desk  for  inspection  by  the  class.  If  prop- 
erly managed,  this  plan  will  prove  a  good  incentive  to 
improvement  in  neatness  in  the  drawing  and  writing. 

Use  of  Pencils. — The  pupils  should  not  be  allowed 
to  write  with  Lhort  pencils.  Particular  care  must  be 
taken  as  to  methods  of  holding  both  pencil  and  pen, 
also  to  the  position  of  the  body  while  writing  and  draw- 
ing, to  avoid  permanent  curvature  of  the  spine  from 
bending  sideways ;  and  serious  injury  to  the  eyesight 
from  inclining  the  head  too  far  forward,  and  holding  it 
too  near  the  desk. 

MANAGEMENT. 

Physical  Training. — The  pupils  in  all  the 
grades  should  be  exercised  daily  in  such  a  manner  as 
to  expand  the  lungs,  develop  the  muscles,  and  impart 
an  easy  and  graceful  carriage  to  the  body.  Calisthenic 
exercises  may  be  employed  for  the  attainment  of  these 
objects. 

Five  minutes  spent  once  an  hour,  or  even  more  fre- 
quently, in  simple  changes  of  the  position  of  the  body, 
by  requiring  the  school  or  class  to  stand  and  to  sit  to- 
gether three  or  four  times  in  succession,  also  to  exercise 
the  arms  briskly,  will  do  much  for  the  physical  comfort 
of  pupils,  and  even  increase  the  progress  in  their  studies. 

The  necessity  of  pure  air  in  a  school-room  is  a  matter 
too  serious  to  be  neglected  by  any  teacher  for  a 
single  hour.  Yet  quite  too  commonly,  even  where 
the  means  for  securing  it  have  been  provided,  te 
carelessly  neglect  ventilation. 


SEVENTH   GRADE, 

(PRIMARY.) 
Time  allowed,  about  five  months. 


LANGUAGE. 

Heading. — In  a  Second  Reader  ;  with  conversational  tones — 
the  use  of  Italic  letters  to  be  explained. 

Phonetics. — Sounds  of  short  words  in  common  use  to  be 
given  by  the  pupils — exercises  to  be  had  for  correcting  indistinct 
enunciation. 

Definitions. — The  meaning  of  words  to  be  given,  chiefly  by 
their  use  in  short  sentences. 

Spelling. — Oral  and  written — words  from  the  reading  les- 
sons ;  also,  other  common  words. 

ARITHMETIC. 
Addition. — With  practical  examples. 

Subtraction. — The  processes  taught  and  practical  examples 
given. 

Multiplication. — Multipliers  from  1  to  12  inclusive. 

Mental  Arithmetic. — Practical  questions  in  Addition,  Sub- 
traction, and  Multiplication.  Also  Oral  Drills  for  rapid  combina- 
tions of  numbers. 

Multiplication  Table. — Continued  through  12  times  12. 
Roman  Numbers. — Reviewed. 

Tables  of  Measure. — United  States  money  ;  time  ;  liquid 
and  dry  measures. 


64  GRADED  COURSE  OF  INSTRUCTION. 

OBJECT  LESSONS. 

Form. — The  polygons,  arc,  radius,  and  other  forms. 
Size. — Comparative,  and  measured. 
Color. — Harmony  of  colors. 
Human  Body. — Organs  of  the  senses. 

Animals. — Comparison  and  simple  classification  by  groups, 
families,  etc. 

Plants. — Shapes  of  roots,  leaves,  flowers,  etc.  Plants  used 
for  food,  etc. 

Objects  and  Qualities.— Continued. 

Occupations. — Trades,  tools,  productions,  commodities,  etc. 

GEOGRAPHY-PREPARATORY  STEPS. 

Place  and  Direction. — First.  Position  of  objects  on  a 
table.  Second.  Position  of  objects  in  the  class-room.  Third. 
Location  and  direction  of  streets  and  other  objects  near  the 
school.  - 

DRAWING  AND  WRITING. 

On  Slates. — Words  and  short  sentences  to  be  written  from 
dictation  ;  Capitals  to  be  used.  Drawing  simple  figures. 

On  Paper. — Simple  words  of  small  letters.  The  pupils  to 
be  taught  to  write  their  names,  with  their  ages,  and  the  date. 


LANGUAGE.  65 

How  TO  TEACH 

SUBJECTS  OF  THE  SEVENTH  GRADE. 


LANGUAGE. 

Reading. — The  methods  given  for  teaching  Read- 
ing in  the  Eighth  Grade  should  be  continued  in  the 
Seventh  Grade.  It  is  exceedingly  important  that  chil- 
dren be  early  trained  to  give  attention  to  the  subject- 
matter  of  what  they  read. 

Should  the  teacher  find  her  class  using  monotonous 
or  unnatural  tones,  several  selections  should  be  made 
of  reading  lessons  that  are  composed  chiefly  of  conversa- 
tions. These  may  be  used  for  training  the  pupils  to 
read  in  easy,  speaking  tones.  Afterwards,  other  selec- 
tions may  follow,  and  special  care  be  taken  to  teach  the 
pupils  to  read  in  a  pleasant,  colloquial  style.  Call  upon 
different  pupils  to  imitate  the  style  of  the  best  readers 
in  the  class. 

Two  extremes,  as  to  the  amount  of  reading  which  the 
class  is  taken  over,  should  be  avoided — that  of  keeping 
the  pupils  too  long  on  the  same  lesson,  and  that  of 
reading  over  many  lessons  without  sufficient  attention 
to  the  matter  and  manner  of  reading.  The  first  extreme 
destroys  the  pupils'  interest  in  this  exercise,  and  pre- 
vents them  from  acquiring  the  habit  of  reading  to  gain 
information ;  the  second  leads  to  carelessness  in  manner, 
and  the  habit  of  reading  without  sufficient  attention  to 
the  subject  of  the  lesson,  and  to  what  is  related  con- 
cerning it. 


66 

The  use  of  Italics  should  be  illustrated  from  the  black- 
board first,  and  afterward  the  pupils  should  be  required 
to  find  examples  in  reading  lessons,  and  to  tell  why  the 
given  Italic  words  are  used. 

Phonetics. — Care  should  be  taken,  in  conducting 
the  exercises  in  sounds,  to  train  the  pupils  in  habits  of 
distinctness  of  enunciation,  and  in  the  use  of  smooth 
tones  of  voice ; — uttering  the  separated  sounds  of  words 
will  aid  in  accomplishing  the  first ;  and  making  the 
sounds  with  varying  pitches  and  different  volumes  of 
voice  will  aid  in  producing  the  second.  Silent  letters 
should  be  pointed  out  by  the  pupils.  They  should 
also  be  required  to  tell  what  sound  each  letter  has  in 
given  words,  and  to  make  the  sound.  These  sounds 
may  be  described  somewhat  as  follows : — Call,  c  has 
the  sound  of  k,  a  has  its  fourth  sound,  the  first  I 
has  its  own  sound,  the  second  /  is  silent.  Bought, 
I  has  its  own  sound,  ou  represent  the  fourth  sound 
of  a,  gli  are  silent,  t  has  its  own. sound.  Think,  tli 
are  sounded  together,  i  has  its  second  sound,  n  has 
the  sound  of  ng,  &has  its  own  sound. 

Definitions. — All  modes  of  teaching  that  will 
allow  pupils  to  give  mere  memorized  definitions,  with- 
out the  ability  to  illustrate  the  meaning  of  the  given 
words  by  their  use  in  complete  sentences  should  be 
avoided.  During  the  exercises  in  definitions,  the 
pupils'  faults  of  language  should  be  corrected. 

Spelling. — The  exercises  for  teaching  spelling  in 
the  Seventh  Grade  may  be  continued  as  in  the  Eighth 
Grade. 


ARITHMETIC.  G7 


ARITHMETIC. 

Addition. — The  exercises  in  this  grade  should  be 
extended  to  examples  with  from  four  to  six  columns  of 
twelve  or  fifteen  figures  each  ;  and  with  occasional 
examples  of  six  or  eight  lines,  embracing  millions. 
Practical  examples,  relating  to  matters  of  daily  occur- 
rence in  business,  should  be  given. 

Exercises  for  training  the  pupils  to  add  without 
counting  should  be  continued  in  this  grade  in  a  man- 
ner similar  to  those  described  for  the  Eighth  Grade,  on 
pages  52,  53  and  54. 

Subtraction. — The  processes  of  Subtraction  may 
be  arranged  in  three  steps,  and  taught  in  their  order, 
as  follows,  viz. : 

First  Step. — With  short  examples  in  which  each  figure 
in  the  subtrahend  represents  a  number  that  is  smaller 
than  the  one  above  in  the  minuend. 

Second  Step. — With  examples  in  which  it  is  neces- 
sary to  take  or  "  to  borrow "  from  the  column  of  a 
higher  denomination. 

Third  Step. — With  examples  having  naughts  in  the 
minuend,  making  it  necessary  to  take  from  the  third 
or  fourth  column  on  the  left. 

The  Second  and  Third  Steps  may  be  illustrated  first 
by  the  use  of  bundles  of  sticks  ;  also  by  the  use  of  cents, 
dimes,  and  dollars,  somewhat  as  follows  :  From  5  dollars, 
4  dimes,  and  2  cents  take  2  dollars  8  dimes  and  5  cents. 
Since  I  have  only  2  cents,  I  must  take  one  of  the  dimes 


68  HO W  TO  TEACH 

and  get  it  changed  into  cents.  This  will  leave  3  dimes, 
and  give  me  12  cents  in  all.  From  the  12  cents  I  can  take 
5  cents,  and  7  cents  will  remain.  I  wish  to  take 
away  8  dimes,  but  find  that  I  have  only  3  dimes  remain- 
ing ;  therefore  I  must  take  one  of  the  dollars  and  get 
it  changed  into  dimes,  which  will  leave  4  dollars,  and 
give  me  13  dimes  in  all.  Now  I  can  take  away  8  dimes 
and  have  5  dimes  left.  Then  I  can  take  2  dollars  from 
4  dollars,  and  have  2  dollars  left.  This  explanation 
may  be  followed  by  another  in  which  the  same  figures 
(542 — 285),  are  used  as  units,  tens,  and  hundreds. 

The  process  of  representing  these  illustrations  may 
be  shown  on  the  blackboard,  thus : 

10  10 

4     3     10  4      3     10 

$0    *d     2c  0h.  j*t.    2  units 

2     8d    5c  285 


$2     5d     7c  257 

• 

Afterward  the  process  of  the  Second  and  Third  Steps 
may  be  further  represented  on  the  blackboard,  with 
common  examples  in  subtraction,  by  cancelling  the 
figures  from  which  one  has  been  taken,  and  writing  the 
remainder  above  it  thus : 


3  10  5  10     5  10  1  10 

9  9  10 
,3  10  10  4  10 

4203   10320 

240000 

1445   15415 

135453 

2818  905104597 

After   this  process,  commonly  called   "borrowing" 

(but  which  is  really  a  change  in  a  part  of  the  higher 

denomination  without  altering  the  value  of  the  entire 

number),  has  been  illustrated  on  the  blackboard  by  the 


ARITHMETIC.  69 

toucher,  the  pupils  should  be  required  to  copy  on  their 
slates  the  same  examples,  also  the  process  of  taking 
from  a  figure  representing  a  number  of  a  higher  denom- 
ination, by  cancelling ;  then  similar  examples  should 
be  given  them  to  write  out  in  full,  that  they  may  become 
familiar  with  the  process  of  taking  from,  by  cancelling. 
Forms  of  illustration  for  explaining  a  subject  should 
be  continued  no  longer  than  may  be  necessary  to  enable 
the  pupils  to  understand  the  subject.  The  process  of 
cancelling  in  illustrating  subtraction  should  be  used  for 
a  few  days  only.  When  it  is  first  dropped,  another  plan 
may  be  adopted  to  represent  the  changes  in  the  figures. 
A  dot  may  be  placed  over  the  figure  in  the  minuend  to 
indicate  that  it  must  be  considered  one  less  in  the  sub- 
traction, thus : 

4263  16320  240050 

1445  15415  135453 


2818  905  104597 

In  subtracting  these  examples,  the  pupil  might  say  : 
3  from  10  leave  7  ;  5  from  14  leave  9  ;  4  from  9  leave  5 ; 
5  from  9  leave  4 ;  3  from  3  leave  0 ;  1  from  2  leaves  1 — 
remainder  104,597. 

This  process  is  shorter  and  less  liable  to  mistakes  in 
practice  than  the  common  way  of  "  borrowing  one " 
from  a  figure  in  the  minuend,  and  "  carrying  one  "  to 
the  next  figure  in  the  subtrahend  ;  besides,  it  prepares 
the  way  for  readily  understanding  the  operations  in 
"  Compound  Numbers." 

Multiplication. — Instruction  in  regard  to  the 
processes  of  multiplication  may  be  presented  in  four 
steps,  as  follows : 


7°  HOW  TO  TEACH 

First  Step. — Give  examples  in  which  no  single  procU 
uct  will  exceed  nine,  as 

243  3,142  3,231  231,232 

223  3 


486  6,284  9,693  693,696 

Second  Step. — Give  examples  in  which  it  will  be  neces- 
sary "  to  carry  "  to  the  next  column,  including  multi- 
pliers of  a  single  figure  only,  from  2  to  5,  as : 

345  4,583  2,435  32,563 

2345 


690          13,749  9,740          162,815 

Third  Step. — Give  examples,  including  naughts  in  the 
multiplicand,  and  use  as  multipliers  6,  7,  8  and  9. 
2,034  3,102  14,020  10,050 

6789 


12,204          21,714          112,160  90,450 

Fourth  Step. — Give  examples  with  multiplicands,  as 
in  the  third  step,  and  use  for  multipliers  10,  11  and  12. 
Teach  the  pupils  where  to  write  the  first  figure  in  each 
partial  product. 

24,065  3,108  40,207 

10  11  12 


240,650  3108  80414 

3108  40207 


34,188          482,484 

First,  illustrate  the  step  on  the  blackboard,  then  give 
the  pupils  similar  examples  for  practice  on  their  slates. 
When  they  have  become  familiar  with  one  step,  proceed 
with  the  next  in  order. 


ARITHMETIC.  71 

Mental  Arithmetic. — The  forms  of  the  answers, 
in  this  grade,  may  very  properly  employ  more  language 
than  in  the  preceding  grade.  The  following  examples 
and  solutions  of  them  will  represent  suitable  forms : 

Examples : — A  man  paid  $12  for  a  barrel  of  flour,  $8 
for  a  ton  of  coal,  and  $5  for  a  load  of  wood ;  how  much 
did  he  pay  for  all  ?  Ans.  He  paid  for  all  the  sum  of 
$12,  $8,  and  $5,  which  is  $25. 

A  farmer  paid  $40  for  a  cow,  and  sold  her  for  $36 ; 
how  much  did  he  lose  ?  Ans,  He  lost  the  difference 
between  $36  and  $40,  which  is  $4. 

What  will  5  oranges  cost,  at  4  cents  each  ?  Ans.  If 
one  orange  costs  4  cents,  5  oranges  will  cost  5  times  4 
cents,  or  20  cents. 

Oral  Drills. — Exercises  for  the  rapid  combination  of 
numbers  should  be  introduced  during  this  grade,  in 
addition  to  a  continuation  of  drills  by  the  "  decades." 

The  class  may  be  trained  to  add  several  numbers,  and 
each  pupil  to  write  the  result  on  a  slate,  or  give  it 
orally.  The  teacher  may  give  7  +  3  +  4  +  5  +  6  +  4  +  2  +  4 
+  5,  are  how  many  ?  In  giving  these  examples  for  ad- 
dition, the  teacher  may  say.  at  first,  7  and  3  and  4  and 
5,  etc.  Subsequently  the  pupils  should  be  taught  the 
meaning  of  the  word  plus,  and  then  these  examples 
may  be  given  thus :  7  plus  3  plus  4  plus  5,  etc. 

Each  pupil,  having  added  these  numbers  mentally, 
should  write  the  sum  obtained  on  the  slate,  and  the 
teacher  should  then  ascertain  which  pupils  have  per- 
formed the  addition  correctly. 

Multiplication  Tables.— When  all  of  these 
tables,  through  12  times  12  have  been  taught  by  the 


72  BOW  TO  TEACH 

three  forms  as  described  in  the  Eighth  Grade,  they  may 
be  reviewed  from  the  blackboard  in  the  following  form, 
the  pupils  reading  thus:  5  times  6  are  30;  6  times  5 
are  30;  9  times  5  are  45;  5  times  9  are  45,  etc. 

5  x  6  are  30 ;  6  x  5  are  30 ;  4  x  8  are  32 ;  8x4  are  32. 

9x5    "    45;  5x9   "   45;  6x8   "  8x6  " 

7x6    "    42;  6x7  "  42;  5xg  "  8x5  " 

4x9"  9x4"  7x9"  9x7 

In  writing  these  tables  on  the  blackboard  for  this 
review,  the  several  products  may  be  omitted,  and  the 
pupils  required  to  give  them  from  memory.  At  this 
stage  the  teacher  should  explain  the  use  of  the  sign  ( x  ) 
of  multiplication. 

Roman  Numbers. —  Review  and  give  further 
applications  of  the  key,  as  indicated  in  the  directions 
relative  to  this  subject  for  the  Eighth  Grade. 

Tables  of  Measure. — The  tables  of  weights  and 
measures  should  be  introduced  first,  by  talking  with 
the  pupils  about  their  experience  in  the  use  of  them, 
and  by  familiar  illustrations  given  by  this  means. 
Thus  the  table  of  United  States  money  may  be  illus- 
trated by  cents,  dimes,  and  dollars ;  that  of  liquid 
measure,  by  what  the  children  know  about  buying  milk, 
molasses,  kerosene,  etc.,  by  the  pint  and  quart ;  that  of 
dry  measure,  by  purchases  at  the  grocery,  by  quarts, 
small  measures,  pecks,  etc. ;  that  of  time,  by  observing 
the  hours  marked  on  the  clock,  and  by  attention  to  the 
days,  weeks,  months,  etc. 

After  talking  with  the  pupils  about  the  uses  of  a 
given  table,  write  it  on  the  blackboard,  and  let  them 
repeat  it ;  then  they  may  copy  the  items  on  slates,  both 


ARITHMETIC. 


73 


in  the  order  of  the  table  and  in  a  different  order.  Con- 
tinue the  repetition  and  copying  until  the  table  is 
thoroughly  learned.  Each  of  the  tables  may  be  present- 
ed and  learned  in  a  similar  manner. 


TABLES  FOR  THE  SEVENTH  GRADE. 


UNITED  STATES  MONEY. 


10  mills  make  1  cent. 
10  cents  "  1  dime. 
10  dimes 


10  dollars 


1  dollar. 
1  eagle. 


LIQUID  MEASURE. 

4  fjills  make  1  pint. 
2  pints     "       1  quart. 
4  quarts  "       1  gallon. 
31}  galls. "     1  barrel. 


100  cents  make  one  dol'ar. 
50      "         "       one-halt  dollar. 
25      "        "       one  quarter  of 

a  dollar. 
75  cents  make  three  quarters 

of  a  dollar. 


DRY  MEASURE. 

2  pints  make  1  quart. 

2  quarts    "    1  small  measure. 

8  quarts    "     1  peck. 

4  pecks      "     1  bushel. 


TIME  MEASURE. 


60  seconds  make  1  minute. 


60  minutes 

24  hours 
7  days 

30  or  31  days 

12  months 

52  weeks 
365  days 
100  years 


1  hour. 
1  day. 
1  week. 
1  month. 
1  year. 
1  year 
1  year. 
1  century 


Days  of  the  Week. 

Sunday, 

Monday, 

Tuesday, 

Wednesday, 

Thursday, 

Friday, 

Saturday. 


Seasons  of  the  Yew. 

Spring, 

Summer, 

Autumn,  or  Fall, 

Winter. 
March,  i 

April,  >•  Are  the  Spring  mos. 
May,     ) 

june>        )    Are    the    Summer 
August,    )       months- 

September,  )AretheAu 
October        V      orFallmonths. 
November,  ) 


December, 

January, 

February, 


Are  the  Winter 
months. 


74  HOW  TO  TEACH 

Revieiv. — In  reviewing  these  tables,  the  teacher  may 
question  the  pupils  somewhat  as  follows  :  How  many 
hours  make  a  day?  How  many  days  make  a  year? 
How  many  days  make  a  week  ?  How  many  weeks 
make  a  year?  How  many  minutes  make  an  hour? 
How  many  months  make  a  year  ?  What  is  the  shortest 
measure  of  time  ?  What  does  it  take  to  make  the  long- 
est measure  of  time  ?  How  many  quarts  make  a  gal- 
lon ?  How  many  quarts  in  three  gallons  ?  How  many 
quarts  make  a  peck  ?  How  many  pints  in  two  quarts  ? 
How  many  quarts  in  two  pecks  ?  Which  is  more,  one 
bushel  or  three  pecks  ? 

A  variety  of  similar  questions  may  be  asked  after  the 
tables  have  been  learned  in  their  order. 


OBJECT  LESSONS. 

ft  is  not  intended  that  each  topic  under  this  heading 
shall  be  made  the  subject  of  a  lesson  each  day ;  but  it 
is  expected  that  a  lesson  will  be  given  each  day  upon 
some  one  of  these  topics,  and  that  these  shall  be  varied 
so  as  to  embrace  all  the  topics  of  the  grade  during  each 
month.  Much  more  time  and  a  greater  number  of  les- 
sons will  be  required  for  some  of  these  topics  than  for 
others. 

Form. — It  is  very  desirable  to  have  the  manner  of 
presenting  the  lessons  on  this  subject  varied  in  each 
succeeding  grade,  so  as  to  avoid  the  possibility  of  mem- 
orizing and  reciting  any  formula.  To  secure  this  end, 
let  the  reviews  of  the  matter  taught  in  preceding  grades 
be  so  conducted  as  to  compel  attention  to  the  shape  of 
the  various  objects. 


OBJECT  LESSONS.  75 

By  requiring  the  pupils  to  describe  the  shape  of  ob- 
jects placed  before  the  class,  the  teacher  will  be  enabled 
to  test  their  knowledge  of  form. 

Size. — This  subject  may  be  illustrated  by  various  ob- 
jects, as  strings  of  different  sizes  arid  lengths,  slips  of 
paper  of  different  lengths  and  widths,  and  small  pieces 
of  wood.  The  pupils  will  obtain  clear  perceptions  of 
size  and  of  length,  by  being  required  to  judge  of  the 
size  and  length  of  objects  before  them,  and  of  lines  on 
the  blackboard,  then  to  measure  these  and  ascertain 
the  approximate  correctness  of  their  estimates.  Draw- 
ing lines  of  given  lengths  on  the  slate,  followed  by  a 
careful  measurement  of  them,  is  a  valuable  means  for 
training  pupils  to  accuracy  in  determining  size  and 
length  by  the  eye. 

Color.—  The  lessons  on  color,  for  this  grade,  should 
lead  the  pupils  to  perceive  that  some  colors  appear  well 
when  placed  side  by  side,  while  others  do  not.  For 
this  purpose  lead  them  to  compare  red  and  green  with 
blue  and  green  ;  blue  and  orange  with  yellow  and  orange; 
yellow  and  purple  with  blue  and  purple,  or  red  and 
purple. 

All  lessons  on  color  should  be  illustrated  with  colored 
objects.  Pieces  of  ribbon,  silk,  worsted,  colored  paper, 
water  colors,  etc.,  may  be  used  for  this  purpose. 

Human  Body. — In  teaching  children  the  names 
and  uses  of  the  organs  of  sense,  and  their  parts,  special 
effort  should  be  made  to  lead  them  to  understand  the 
subject  by  means  of  observations  made  witli  their  own 
organs  of  sense.  The  actual  seeing,  hearing,  feeling, 
tasting,  and  smelling  of  objects  teach  children  facts 


76  HOW  TO  TEACH 

which  it  is  impossible  to  convey  to  their  minds  by 
means  of  the  memorizing  of  language,  however 
thorough  and  precise. 

Animals. — The  lessons  on  this  subject  should  lead 
the  children  to  notice  the  most  distinguishing  points  in 
the  structure  of  animals,  and  to  see  how  their  structure 
is  adapted  to  their  habits  of  life ;  for  instance,  how  the 
webbed  feet  of  some  birds  fit  them  for  swimming,  and 
how  the  long  legs  of  others  fit  them  for  wading ;  how 
the  strong  claws  and  strong  beaks  of  some  birds  enable 
them  to  feed  on  flesh  ;  how  the  cushion-like  feet  of  the 
cat  enable  it  to  walk  noiselessly  about  in  search  of  its 
prey ;  how  the  teeth  of  the  cat  and  dog  are  fitted  for 
tearing  flesh,  while  those  of  the  rat  and  squirrel  are 
formed  for  cracking  nuts  and  gnawing  hard  sub- 
stances. 

The  chief  aim  of  these  lessons  being  to  train  the  pu- 
pils in  habits  of  observing  nature,  so  that  they  may  be 
enabled  to  gain  therefrom  the  most  useful  knowledge, 
the  exercises  should  be  conducted  in  such  a  manner  as 
to  lead  them  to  notice  accurately  the  structure  and 
habits  of  the  various  animals  that  come  within  their 
own  observation.  The  facts  thus  learned  should  be,  by 
the  aid  of  the  teacher,  properly  classified,  as  a  founda- 
tion for  subsequent  study  of  the  same  subject. 

Prang's  Natural  History  Series,  with  the  "Man- 
ual" which  accompanies  it,  will  be  found  a  valuable  aid 
in  giving  instruction  on  Animals  and  Plants. 

Plants. — The  lessons  on  plants,  in  this  grade,  may 
appropriately  lead  the  pupils  to  learn  the  most  common 
shapes  of  roots,  as  turnip-shaped,  branching,  fibrous, 


OBJECT  LESSONS.  77 

conical,  tuberous,  etc. ;  also  the  shapes  of  leaves,  as 
needle-shaped,  arrow-shaped,  egg-shaped,  heart-shaped, 
hand-shaped,  etc.;  also  the  common  shapes  of  flowers, 
as.  funnel-shaped,  bell-shaped,  pink-shaped,  butterfly- 
shaped,  helmet  shaped,  cross-shaped,  etc.  By  suitable 
exercises  the  teacher  should  also  direct  the  attention  of 
the  pupils  to  plants  which  are  used  for  food,  and  lead 
them  to  observe  their  mode  of  growth,  form,  uses,  etc. 

Objects  and  Qualities. — Two  distinct  classes  of 
exercises  may  be  given  under  this  heading.  One  con- 
sists in  training  the  pupils  to  distinguish  given  quali- 
ties, by  using  several  objects  having  the  same  quality, 
for  illustration ;  the  other,  which  is  more  appropriate 
for  review  exercises,  requires  the  pupils  to  ascertain 
what  qualities  a  given  object  possesses.  Instruction  on 
this  subject  cannot  be  considered  complete  Avithout  the 
use  of  both  of  these  classes  of  exercises,  in  their  proper 
order. 

Observation  and  Comparison.  —  Habits  of 
observing  various  objects,  and  noticing  their  several 
sliapes,  colors,  qualities  and  materials  of  which  they  are 
made,  are  exceedingly  useful  as  a  means  of  gaining 
knowledge ;  yet  habits  of  comparing  two  or  more  ob- 
jects, and  observing  what  qualities,  shapes,  colors  and 
materials  they  possess  in  common,  constitutes  an  ad- 
vanced stage  of  development  which  not  only  adds  addi- 
tional power  of  gaining  knowledge,  but  gives  to  the 
possessor  practical  ability  in  whatever  sphere  of  life  that 
person  may  be  placed. 

In  the  preceding  grades  the  pupils  have  been  taught 
to  distinguish,  and  to  name  the  common  forms,  colors, 


78  HOW  TO  TEACH 

and  most  obvious  qualities.  It  is  therefore  appropriate 
that  they  now  should  be  trained  to  discover  which 
of  these  forms,  colors,  and  qualities  may  be  found  in 
given  objects  to  which  their  special  attention  may  be 
directed. 

This  kind  of  training  should  be  so  conducted  as  to 
develop  the  individual  powers  of  the  pupils.  To  ac- 
complish this,  the  teacher  must  avoid  asking  such 
questions  as  might  suggest  to  the  pupil  what  to  say, 
rather  than  leave  him  to  discover  the  shape,  color,  qual- 
ity, or  material  without  aid.  The  teacher  should  aim 
to  train  the  pupils  to  discover  the  principal  character- 
istics of  an  object,  instead  of  telling  them  what  those 
characteristics  are,  and  then  asking  them  questions  to 
see  if  they  remember  them. 

Steps  somewhat  like  the  following  are  appropriate  to 
be  taken  by  the  teacher : — 

First.  Write  on  the  blackboard  the  words,  Materi- 
als, Shapes,  Colors,  Qualities,  leaving  room  to  write 
other  words  under  each.  Then  place  some  object  be- 
fore the  pupils,  as  a  common  slate,  and  request  them  to 
tell  what  materials,  shapes,  colors,  and  qualities  they 
observe  in  it.  As  these  are  mentioned  by  the  pupils, 
singly,  the  teacher  may  write  the  word  on  the  black- 
board under  its  appropriate  heading.  When  the  lesson 
is  finished,  the  blackboard  will  contain  something  like 
the  following : 

Materials.        Shapes.          Colors.          Qualities. 

slate,  oblong,  black.  opaque, 

wood,  right  angles.  brittle, 

iron.  combustible. 


OBJECT  LESSONS.  79 

Occupations.  —  The  exercises  on  this  topic  should 
cause  the  children  to  ascertain  the  names  of  tools  used 
in  different  occupations,  and  what  is  done  with  these 
tools;  also  what  articles  are  made  or  produced.  For 
instance,  the  teacher  might  write  on  the  blackboard 
the  word  carpenter,  shoemaker,  or  painter,  and  request 
the  pupils  to  ascertain  what  tools  are  used  by  those  who 
pursue  the  given  trade,  and  report  on  the  next  day  after 
the  subject  is  thus  assigned  —  the  teacher  writing  the 
names  of  tools  mentioned  by  the  pupils  on  the  black- 
board, and  the  pupils  copying  them  subsequently  on 
their  slates.  These  exercises  will  furnish  an  excellent 
opportunity  for  practice  in  observation,  and  in  describ- 
ing what  has  been  seen.  They  may  be  made  useful, 
also,  for  first  lessons  in  composition. 

The  form  in  which  these  lessons  may  be  placed  on 
the  blackboard  is  represented  by  the  following  :  — 

Name  of  Occupation.  Tools  used. 

r-««  I  Saw»  Plane,  Chisel,  Auger,  Awl, 

ter'  \  Hammer,  Mallet,  Rule,  Square. 


Shoemaker.  ,a,  Aw,. 


{E&L±S. 


CABINET-MAKER. 

Tools  Used.  Materials.  Articles  Made. 

Saws,  Black-walnut,  Tables, 

Planes,  Mahogany,  Stands, 

Chisels,  White  Oak,  Bureaus, 

Bits,  Cherry,  Sofas, 

Hand-screws,  Pine,  Bedsteads, 

Squares,  Glue,  Desks. 

Scrapers,  Varnish,  etc.  Book-cases, 

Mallet.  Sideboards. 


80  HOW  TO  TEACH 


GEOGRAPHY- PREPARATORY  STEPS. 

Place  and  Direction. —  The  exercises  in  this 
subject  must  be  objective  in  their  character  ;  and  they 
should  be  conducted  with  a  view  to  prepare  the 
pupils  for  understanding  the  elementary  steps  of  Geog- 
raphy. The  manner  of  giving  the  lessons  in  steps  will 
prove  most  useful  to  the  pupils. 

First  Step. — Train  the  pupils  to  observe  and  de- 
scribe the  position  of  objects  on  the  table  in  front 
of  them,  using  the  terms  right,  left,  front,  back,  front 
left-hand  corner,  back  right-hand  corner,  etc.  Then 
let  the  teacher  represent  the  positions  of  these  objects 
on  the  blackboard.  Afterwards  request  the  pupils  to 
copy  the  representation  from  the  blackboard,  on  their 
slates. 

Second  Step. — Train  the  pupils  to  notice  and  describe 
the  positions  of  the  parts  of  the  class-room,  and  of  the 
principal  articles  in  it,  as :  door,  windows,  blackboard, 
seats,  table,  chair,  closet,  etc. 

The  teacher  should  draw  the  outlines  of  the  class- 
room, and  represent  the  positions  of  the  articles  in  it,  on 
the  blackboard,  at  the  same  time  requiring  the  pupils 
to  tell  where  to- place  the  representation  of  each  object, 
before  drawing  it.  Subsequently  the  pupils  should 
copy  the  same  on  their  slates. 

Third  Step. — Teach  the  pupils  the  location  of  the 
streets  near  the  school,  and  require  them  to  observe  and 
tell  in  what  streets  they  go  while  on  their  way  to  and 
from  school.  The  terms  of  direction,  as  east,  west, 
north,  south,  may  be  introduced  in  this  step,  and  the 


DRAWING  AND  WRITING.  81 

Points  of  Compass  taught.  Kepresent  the  locations  of 
streets,  buildings  near  the  school,  etc.,  on  the  black- 
board, and  let  the  pupils  copy  them,  as  before. 


DRAWING  AND  WRITING. 

On  Slates. — The  lessons  in  Drawing  and  Writing, 
for  this  grade,  must  necessarily  be  simple,  yet  they 
should  be  progressive,  and  so  arranged  as  to  lead  to  a 
proper  training  of  the  eye  and  hand  ;  indeed  this  train- 
ing should  be  made  a  prominent  object.  The  black- 
board should  be  used  much  in  illustrating  the  exercises 
of  both  drawing  and  writing.  Enlarged  copies  of  good 
drawing  cards,  also  simple  drawings  from  objects  may 
be  made  on  the  blackboard,  and  the  pupils  required  to 
copy  them  on  their  slates. 

Care  should  be  taken  to  teach  the  pupils  proper  posi- 
tions for  sitting,  for  holding  their  slates,  also  for  the 
hand  and  fingers  in  holding  the  pen  or  pencil. 

On  Paper* — When  writing  is  commenced  with 
ink,  do  not  confine  the  pupils  too  long  to  making  the 
simple  elements  of  letters ;  let  them  learn  to  write 
simple  words  as  soon  as  practicable.  It  is  not  necessary 
that  the  pupils  should  write  all  the  lines  under  each 
copy  of  a  common  writing-book.  Whenever  the  pupils 
have  made  sufficient  progress  to  be  able  to  proceed  with 
the  next  copy  in  order,  let  them  go  on  with  it.  But 
there  should  be  system  in  the  progress ;  all  the  pupils 
in  the  grade  should  receive  instruction  relative  to  the 
same  points,  and  write  the  same  words  simultaneously ; 
thus  all  will  attend  to  the  same  thing,  at  the  same  time, 
and  proceed  to  a  new  lesson  together.  Faults  in  writ- 


82  JIOW  TO  TEACH. 

ing-  should  be  pointed  out  and  illustrated  on  the  black- 
board, and  such  directions  given  as  will  enable  the 
pupils  to  correct  those  faults. 

Before  leaving  this  grade,  the  pupils  ought  to  be  able 
to  write  simple  words  neatly  with  the  pen ;  and  to 
write  their  own  names,  and  their  age ;  also  the  day  of 
the  month,  and  the  year,  in  a  proper  form  for  dating  a 
letter.  They  should  also  be  able  to  write  familiar 
worus,  and  short  sentences  from  dictation,  readily  and 


SIXTH    GRADE. 

(HIGHEST  PRIMARY.) 
Time  allowed,  about  five  months. 


LANGUAGE. 

Reading. —  f-econd  Reader  completed,  or  an  easy  Third 
Reader  commenced. 

Phonetics. — Words  to  be  analyzed  by  sounds ;  names  of 
the  sounds  to  be  stated ;  faults  of  enunciation  to  be  cor- 
rected. 

Definitions. — The  meaning  of  words  to  be  given  orally, 
and  in  writing. 

Spelling. — Words  from  the  reading  lessons,  also  familiar 
words,  and  short  sentences  from  dictation,  both  orally,  and  by 
writing  on  slates. 

ARITHMETIC. 

Addition  and  Subtraction  reviewed. 
Multiplication  continued  through  multipliers  of  five  figures. 

Division. — Both  the  long  and  the  short  forms.  Simple 
practical  examples  to  be  given  in  each  of  these  rules. 

Mental  Arithmetic. — Practical  examples  in  each  of  the 
four  simple  rules. 

Division  Table. — Taught  in  connection  with  a  review  of 
the  Multiplication  Table. 


84  HO  W  TO  TEACH 

Tables  of  Weight  and  Measure.— The  tables  of  Com- 
mon or  Avoirdupois  Weight,  of  Long,  Cloth,  and  Surface  meas- 
ure, also  a  miscellaneous  table  to  be  taught,  and  those  of  the 
Seventh  Grade  to  be  reviewed. 


OBJECT  LESSONS. 

Form. —  The  shapes  of  objects  to  be  compared  and  described, 
and  their  resemblances  and  differences  stated. 

Human  Body. — Lessons  to  be  continued  as  in  previous 
grades,  and  extended. 

Animals. — Comparison  and  classification  continued;  also 
size,  and  where  found. 

Plants. — Parts  of  leaves;  shapes  of  margins;  shapes  of 
flowers  ;  and  comparison  of  members  of  the  same,  and  of  differ- 
ent families  of  flowers. 

Objects. — Various  objects  to  be  examined  and  their  shape, 
color,  most  obvious  qualities,  and  properties  to  be  stated.  The 
distinctions  between  minerr  vegetable,  and  animal  substances 
to  be  taught. 

Occupations. — Exercises  to  give  the  pupils  habits  of  observ- 
ing and  describing  common  productions,  commodities,  etc. ;  also 
to  give  them  ideas  of  the  exchange  and  sale  of  these. 


GEOGRAPHY. 

First  Step. — The  location  and  direction  from  the  school  of  the 
most  prominent  objects  near  the  school,  and  of  the  places  in  its 
vicinity. 

Second  Step. — Definitions  relating  to  the  forms  of  land  and 
water,  from  cards,  blackboard,  and  outline  maps. 


DRAWING  AND  WHITING.  85 

Third  Step. — Teach  the  name  of  the  city  or  town,  the  county, 
and  state  in  which  the  pupils  live,  and  also  of  the  places  in  the 
vicinity,  showing  their  location  on  an  outline  map. 

Fourth  Step. — Teach  the  shape  of  the  Earth  by  means  of  a 
globe  and  hemisphere  maps. 

Fifth  Step. — Teach  the  location  of  the  principal  countries  by 
associations  with  their  most  familiar  animals,  inhabitants,  and 
productions  ;  also  the  location  of  the  warm  and  the  cold  coun- 
tries. 


DRAWING  AND  WRITING. 

On  Slates. — Writing  to  be  continued  as  in  the  Seventh 
Grade. 

Oti  Paper. — Writing  in  books,  from  copies,  with  necessary 
instructions  in  regard  to  the  position  of  the  body,  hand,  and 
paper. 


86  HOW  TO  TEACH 


How  TO  TEACH 


SUBJECTS     OF    THE    SIXTH     GRADE. 


LANGUAGE. 

Heading. — Before  a  new  lesson  is  read,  the  unfa- 
miliar and  difficult  words  in  it  should  be  selected,  written 
on  the  blackboard,  carefully  pronounced  by  the  teacher, 
and  repeated  by  the  pupils ;  also  both  the  meaning  and 
the  spelling  of  these  words  should  be  taught; — afterwards 
the  teacher  should  request  the  pupils  to  find  the  same 
words  in  their  reading  lessons,  and  to  pronounce  them 
again. 

Occasionally  call  upon  a  pupil  to  read  while  the  other 
members  of  the  class  close  their  books  and  listen ;  then, 
at  the  close  of  the  reading  request  those  who  listened 
to  state  the  substance  of  what  was  read.  This  exer- 
cise will  train  pupils  to  habits  of  attentive  listening, 
and  to  a  proper  regard  to  the  subject-matter. 

In  efforts  to  correct  the  faults  of  a  class  in  reading, 
select  first  the  most  common  fault,  and  direct  almost 
exclusive  attention  to  that  until  it  is  understood  and 
easily  overcome  by  the  pupils.  Then  select  another 
common  fault  and  proceed  in  the  same  manner,  giving 
attention  to  the  first  one  also.  Afterward  select  another 
fault,  and  proceed  in  a  similar  manner,  giving  attention 
to  the  three.  By  this  means  a  class  may  be  trained  to 
perceive  and  overcome  faults  in  reading,  much  more 
effectively  than  by  trying  to  point  out  half  a  dozen 
different  kinds  of  faults  at  once. 


LANGUAGE.  87 

Phonetics* — The  phonic  analysis  of  words  should 
train  the  pupils  readily  to  distinguish  and  make  all  the 
sounds  in  given  words,  also  to  determine  which  letters 
are  silent.  It  should  also  lead  the  pupils  to  such  habits 
of  distinctness  in  articulation  as  will  remove  the  fault 
of  neglecting  to  sound  the  final  consonants,  as  d  in  ant?, 
sen^;  r  in  far,  car;  ing  in  singing,  eaiing,  etc.;  also 
the  errors  of  sounding  improperly  both  consonants  and 
vowels  in  the  pronunciation  of  common  words. 

No  other  means  is  so  efficient  for  training  the  organs 
of  speech  in  clearness  and  correctness  of  articulation 
as  that  of  elementary  sounds.  By  suitable  exercises 
with  these,  the  ear  and  the  vocal  organs  may  be  suc- 
cessfully cultivated,  and  the  means  furnished  to  the 
pupils  for  determining  what  are  the  correct  sounds 
of  the  language,  how  to  produce  them,  and  the  ability 
to  cultivate  their  own  organs  of  speech  and  tones  of 
voice. 

Definitions. — Exercises  in  which  the  definitions 
are  to  be  written  on  slates,  in  short  sentences,  should  be 
introduced  in  alternation  with  oral  exercises  of  a  simi- 
lar character.  It  is  desirable  that  an  oral  exercise  of 
this  kind,  given  as  a  lesson  on  one  day,  should  be  fol- 
lowed 011  the  next  day  with  the  same  words  to  be  defined 
in  a  written  exercise,  thus  training  the  pupils  to  write 
as  well  as  to  talk. 

In  the  oral  definitions,  let  the  pupils  be  required  to 
tell  what  given  words  mean,  in  their  own  language,  as 
well  as  to  use  them  in  short  sentences.  One  pupil 
may  be  requested  'to  give  a  brief  definition  of  a  word, 
another  pupil  to  use  it  in  a  sentence,  and  another  one 
to  illustrate  its  meaning  by  describing  its  use.  Habits 


HO  W  TO  TEACH 

of  reciting  formal,  memorized  definitions  would  be 
avoided  by  using  thus  several  modes  of  giving  the  mean- 
ing of  the  same  word,  and  the  pupils  would  learn  to 
define,  and  use  words  intelligently. 

Spelling. — More  attention  should  be  given  to  writ- 
ten than  to  oral  spelling,  in  this  grade.  Words  may 
be  dictated  for  the  pupils  to  write  on  their  slates ;  short 
sentences  may  be  given  for  the  same  purpose ;  the  pu- 
pils may  be  requested  to  write  the  names  of  classes  of 
objects,  as  names  of  kinds  of  food,  articles  of  clothing, 
of  furniture,  kinds  of  tools,  names  of  occupations,  of 
animals,  of  trees,  of  fruits,  of  articles  that  may  be  pur- 
chased at  a  grocery  etc.,  etc.  These  exercises  will  enable 
pupils  to  learn  the  spelling  of  a  large  class  of  words 
in  common  use. 


ARITHMETIC. 

Addition  and  Subtraction. — It  is  intended  that 
the  processes  of  adding  and  subtracting  shall  have  been 
taught  so  thoroughly,  before  the  pupils  are  placed  in 
the  Sixth  Grade,  that  each  one  will  be  able  to  add  and 
subtract  with  facility,  and  with  a  good  degree  of  accu- 
racy. Now,  special  pains  should  be  taken  to  teach  the 
uses  of  Addition  and  Subtraction  by  means  of  prac- 
tical examples.  A  brief  review  of  these  rules  should 
be  had  at  least  once  each  week,  during  the  entire  term 
of  the  Sixth  Grade. 

Multiplication. — Instruction  may  be  arranged 
and  presented  in  three  steps,  as  follows : 


ARITHMETIC.  89 

First  Step. — Give  examples  with  multipliers  of  two 
figures  only — 12  to  99. 

Second  Step. — Give  examples  with  multipliers  of  three 
figures — 100  to  999 — including  some  with  naughts  in 
the  multiplicand. 

Third  Step. — Give  examples  with  multipliers  of  four 
or  five  figures,  containing  one  or  more  naughts.  Both 
the  multiplicand  and  multiplier  should  be  so  varied  as 
to  include  all  the  difficulties  arising  from  the  different 
positions  of  naughts. 

Pupils  should  be  carefully  trained  to  write  the  first 
figure  of  each  partial  product  in  its  proper  place — under 
the  figure  used  as  a  multiplier. 

Review  each  step  with  practical  examples,  embracing 
transactions  that  come  within  the  observation  of  the 
pupils. 

Division. — This  rule  can  be  taught  most  thor- 
oughly by  commencing  the  instruction  with  the  "  Long 
Division  "  form,  and  using  a  small  number  for  a  divisor. 
Four  Steps  will  indicate  the  methods  and  order  for 
teaching  Division. 

First  Step. — Give  examples  in  which  each  figure  of 

the  dividend  will  contain  the  divisor  without  a  remain- 
der, thus : 

2)486(243  3)963(321 

4_  9_ 

08  06 

8_  Q_ 

06  03 

6  .3 

0  0 


90  HOW  TO  TEACH 

Second  Step. — Give  examples  with  the  divisor  less 
than  ten,  in  which  remainders  will  occur  during  the 
partial  divisions,  thus : 

4)976(244  8)9856(1232 

8_  8_ 

17  18 

16_  18_ 

16  25 

H  24_ 

0  16 

•16_ 
0 

Tliird  Step. — Give  examples  with  divisors  from  10  to 
15,  then  teach  the  "  Short  Division  "  form  ;  and  subse- 
quently require  the  pupils  to  use  the  Short  form  for 
all  examples  where  the  divisor  does  not  exceed  12. 

10) 2540 (254  11)  3564 (324  15) 345 (23 

20_  33_  30_ 

54  26  45 

50  22  45_ 

40  44  0 

40_  _44_ 
0  0 

In  illustrating  the  Short  Division  form,  give  the  same 
examples,  each  with  only  one  figure  in  the  divisor,  to  be 
worked  by  both  the  Long  and  the  Short  forms,  taking 
care  to  arrange  the  two  modes  so  that  the  difference 
in  their  lengths  shall  readily  illustrate  Avhy  one  form 
is  called  "  Long  Division,"  and  the  -other  one  "  Short 
Division." 

Fourth  Step. — Give  examples  with  divisors  embracing 
numbers  from  15  to  50.  Arrange  these  examples  so 


ARITHMETIC.  91 

that  different  quotients  shall  contain  naughts  in  various 
positions.  Each  step  should  be  amply  illustrated  on 
the  blackboard,  by  the  teacher,  then  a  sufficient  num- 
ber of  examples  given  to  furnish  the  practice  necessary 
to  enable  the  pupils  to  understand  it,  before  proceeding 
to  the  succeeding  step. 

Teachers  should  aim  first  to  cause  their  pupils  to  un- 
derstand the  processes  of  the  several  rules,  then  to  use 
them  in  an  intelligent  manner.  The  object  of  the  drills, 
by  means  of  numerous  examples,  should  be  accuracy, 
first;  rapidity,  second;  never  rapidity  by  neglecting 
accuracy.  Practical  examples  should  be  given,  in  each 
of  the  rules,  to  insure  an  understanding  of  their  uses. 

MENTAL  ARITHMETIC. — The  forms  for  answering 
questions  in  addition,  subtraction,  and  multiplication 
in  this  grade,  may  be  the  same  as  for  the  Seventh  Grade, 
which  see.  Questions  may  also  be  introduced  which 
will  require  both  addition  and  subtraction  for  their 
solution,  as : 

Henry  had  18  cents ;  he  gave  two  cents  for  pencils, 
and  6  cents  for  a  sponge ;  how  many  cents  had  he  left  ? 
Answer. — Henry  spent  the  sum  of  2  cents  and  6  cents, 
which  is  8  cents.  He  then  had  left  the  difference  be- 
tween 8  cents  and  18  cents,  which  is  10  cents. 

Division. — How  many  tops  at  3  cents  each  can  be 
bought  for  12  cents  ?  Ans.— As  many  tops  as  3  cents, 
the  price  of  one  top,  is  contained  times  in  12  cents, 
which  is  four  times ;  therefore  four  tops  can  be 
bought. 

If  2  apples  cost  4  cents,  what  will  one  apple  cost  ? 
Ans. — If  2  apples  cost  4  cents,  one  apple  will  cost  one- 
half  of  four  cents,  which  is  two  cents. 


Division  Tables. — The  Multiplication  Table  may 
be  so  reviewed  as  to  enable  the  pupil  to  learn  the  Di- 
vision Table  easily.  The  following  form  will  illustrate 
methods  for  accomplishing  this : 

4x7  are  28 ;  4  in  28  seven  times. 

7x4    "    28;  7  in  28  four 

6x7    "    42 ;  6  in  42  seven    " 

7x6     "    42 ;  7  in  42  six         "         etc. 

This  review,  combining  Multiplication  and  Division, 
should  be  continued  through  each  of  the  tables;  and 
subsequently  the  teacher  may  review  the  Division  Tables 
by  questions  similar  to  the  following : 

How  many  eights  in  32  ?  How  many  sevens  in  56  ? 
How  many  nines  in  45  ?  How  many  tivelves  in  108  ? 
How  many  eights  in  96?  How  many  fives  in  60? 
How  many  sixes  in  54  ?  etc. 

Tables  of  Weight  and  Measure. — The  tables 
may  be  taught  as  in  the  Seventh  Grade,  first,  objectively, 
then  memorized  in  order;  and  all  the  tables  of  both 
the  Seventh  and  Sixth  Grades  should  be  reviewed  thor- 
oughly during  this  grade. 


TABLES   FOR   THE    SIXTH    GRADE. 


COMMON,  OR  AVOIRDUPOIS  WEIGHT. 

16  ounces  make  1  pound. 
8      "  "1  half  pound. 

4      "  '•     1  quarter  of  a  pound 

100  pounds     "     1  hundred  weight. 
20  hundred  weight  make  1  ton. 
2000  pounds  make  1  ton. 


LONG  MEASURE. 

12   inches  make  1  foot. 

3    feet 

1  yard. 

16i  feet 

Irod. 

5J  yards 

Irod. 

40   rods 

1  furlong. 

8   furlongs 

1  mile. 

320   rods 

1  mile. 

3   miles 

1  league. 

ARITHMETIC. 


93 


CLOTH  MEASURE. 

3  feet    make  1  yard. 

36  inches    '*    1 
18        "       "    i 

9        "       "    } 


4  quarters  "    1 


12  things  make  1  dozen. 


SURFACE  MEASURE. 

144  square  inches  make  1  square  foot. 
9       "     feet          "     1       "    yard. 
30J      "     yards       "     1       "     rod. 
160       "     rods         "     1  acre. 
640  acres  "     1  square  mile. 


MISCELLANEOUS  TABLE. 


144     " 

1  gross. 

12  dozen 

1     " 

12  gross 

1  great  gross. 

»  things 

1  score. 

24  sheets 

1  quire  of  paper. 

20  quirea 

1  ream. 

32  pounds 

1  bushel  of  oats. 

48  pounds  make  1  bushel  of  barley, 
[or  buckwheat. 

58      "  "1  bushel  of  corn. 

60      "  "1       "       "  wheat 

196     "  "1  barrel  of  flour. 

200      "  "1       "      "     pork, 

[beef,  or  fish. 


2=0 


of  salt. 


Review. — After  these  tables  have  been  thoroughly 
learned  in  order,  the  teacher  may  conduct  brief  reviews 
of  those  of  both  the  Seventh  and  Sixth  Grades,  by 
questions  somewhat  like  the  following : 

How  many  inches  in  three-quarters  of  a  yard  ?  How 
many  yards  in  one  rod  ?  How  many  rods  in  a  mile  ? 
How  many  square  inches  in  a  square  foot  ?  How  many 
buttons  in  a  gross  ?  How  many  sheets  of  paper  in  a 
quire?  How  many  in  half  of  a  .quire  ?  How  many 
pounds  in  a  barrel  of  flour  ?  Which  is  heavier,  a  bushel 
of  wheat  or  a  bushel  of  corn  ?  How  many  pounds  in 
half  of  a  ton?  How  many  pecks  in  two  bushels? 
How  many  quarts  in  two  gallons  ?  How  many  days 
in  a  year  ?  How  many  months  in  half  of  a  year  ?  How 
many  square  feet  in  a  square  yard  ?  Which  is  longer, 
six  feet  or  two  yards  ? 


94  HOW  TO  TEACH 


OBJECT    LESSONS. 

The  various  topics  embraced  in  Object  Lessons  furnish 
far  more  effective  means  for  thoroughly  developing  the 
minds  of  children  than  any  exercises  that  pertain  ex- 
clusively to  reading,  spelling,  arithmetic,  etc.  Children 
whose  powers  of  mind  have  been  developed  by  proper 
training,  so  that  they  observe,  compare,  classify,  and 
describe  intelligently  whatever  comes  within  the  range 
of  their  observation,  will  learn  every  subject  more  easily 
than  they  could  have  done  without  such  training.  For 
these  reasons  suitable  attention  should  be  given  in  each 
grade,  to  all  the  topics  embraced  under  the  head  of 
Object  Lessons.  And  teachers  should  keep  promi- 
nently in  view  the  importance  of  these  lessons  as  a 
means  for  proper  mental  discipline,  and  not  regard  the 
knowledge  gained  by  the  exercises  as  comprising  their 
chief  value. 

Due  attention  to  these  considerations  will  lead  teach- 
ers to  regard,  as  of  much  importance,  the  manner  of 
giving  the  lesson. 

Form. — The  character  of  the  instruction  in  this 
subject,  especially  so  far  as  it  pertains  to  learning  to 
recognize  and  describe  the  various  forms  and  solids,  need 
not  differ  materially  in  the  Seventh  and  Sixth  Grades. 
However,  when  the  several  shapes  required  have  been 
learned  by  means  of  the  regular  forms  and  solids  pro- 
vided for  this  purpose,  the  time  given  to  this  topic  should 
be  chiefly  devoted  to  comparing  and  describing  other 
objects  by  their  shape,  stating  wherein  those  compared 
resemble  each  other,  and  wherein  they  differ. 


OBJECT  LESSONS.  05 

Human  Body. — The  lessons  in  this  grade  should 
be  conducted  so  as  to  review  the  i'acts  learned  in  pre- 
vious grades,  and  also  so  as  to  extend  the  pupils'  knowl- 
edge of  the  laws  of  health,  especially  so  far  as  these 
pertain  to  the  condition  of  the  skin,  habits  of  cleanli- 
ness, and  the  manner  of  eating. 

Animals* — The  manner  of  conducting  the  lessons 
on  this  topic  for  the  Sixth  Grade  classes  may  be  nearly 
the  same  as  that  for  the  Seventh  Grade  ;  but  the  pupils 
in  this  grade  should  be  led  to  consider  a  greater  num- 
ber of  animals  than  those  in  the  previous  one,  and  to  ob- 
serve more  carefully  the  peculiarities  of  structure,  etc., 
with  a  vieAV  to  extending  their  knowledge  of  classifi- 
cation. 

To  aid  the  pupils  in  making  groups  of  animals,  by 
simple  classification,  let  the  teacher  write  on  the  black- 
board the  following  and  similar  names  for  groups: 

Swimming  Birds,  Cud-chewing  Quadrupeds, 

Wading  Birds,  Flesh-eating  Quadrupeds, 

Climbing  Birds,  Gnawing  Quadrupeds, 

Scratching  Birds,  Insects, 

Flesh-eating  Birds,  Reptiles, 

Perching  Birds.  Fish. 

Then  request  the  pupils  to  give  the  names  of  animals 
to  be  written  under  each  heading. 

These  lessons  relative  to  animals  should  lead  the 
children  to  make  comparisons  as  to  form,  structure, 
habits,  size,  etc.,  and  to  learn  in  what  countries  and 
localities  the  various  birds  and  quadrupeds  may  be 
found. 

PRANG'S  Natural  History  Series  will  be  found 
adapted  to  giving  this  instruction. 


06  HOW  TO  TEACH 

I*lant8» — The  lessons  on  this  subject  in  the  Sixth 
Grade  may  lead  the  pupils  to  consider  the  parts  and 
uses  of  leaves,  their  margins,  parts  and  uses  of  flowers, 
as  petals,  stamens,  pistil,  etc. ;  the  comparison  of  pinks, 
lilies,  fruit-blossoms,  etc.,  with  a  view  to  noticing  re- 
semblances in  those  of  the  same  family,  and  differences 
in  others;  also  kinds  of  fruits  which  the  pupils  have 
seen — the  names  to  be  written  on  the  blackboard,  and 
copied  by  the  pupils  on  their  slates,  as  a  spelling  exer- 
cise. The  names  of  fruits  and  grasses  used  for  food, 
etc.,  may  be  written  in  groups.  Like  the  lessons  on 
animals,  these  exercises  should  be  so  conducted  as  to 
lead  the  pupils  to  form  habits  of  carefully  studying  na- 
ture, as  a  means  of  pleasure  and  as  a  source  of  knowl- 
edge; therefore,  the  time  selected  for  giving  the  lessons 
on  plants,  etc.,  should  be  during  the  seasons  when  the 
pupils  can  personally  examine  these  objects. 

The  teacher  would  do  well  to  consult  two  excellent 
works  by  Prof.  GUAY — How  Plants  Grow  ;  and  How 
Plants  Behave. 


Objects. — In  the  Sixth  Grade  the  lessons  on  objects 
should  include  their  descriptions  as  to  form,  color,  and 
most  obvious  qualities.  In  this  connection,  it  is  desir- 
able that  the  pupils  be  led  to  consider  what  qualities 
are  necessary  in  the  substances  used  for  various  tools, 
utensils,  articles  of  dress,  etc.  For  instance,  what  qual- 
ity is  necessary  for  wagon  and  other  springs  ?  What 
qualities  make  sponge  useful  ?  AVhat  qualities  render 
salt  and  sugar  valuable  ?  What  qualities  give  value  to 
India  rubber  ?  What  qualities  give  value  to  glass  ? 
What  to  steel  ?  to  iron  ?  Why  will  not  lead  make 
good  springs,  or  knives  ? 


OBJECT  LESSONS.  97 

The  lessons  under  this  topic  should  cause  the  pupils 
to  consider  wherein  animals,  vegetables,  and  minerals 
differ  from  each  other.  Pupils  will  understand  this 
subject  more  thoroughly  by  presenting  the  instruction 
in  three  steps. 

First  Step. — Request  the  pupils  to  observe  slate-pen- 
cils, pieces  of  stone,  iron,  lead,  chalk,  and  various  pieces 
of  wood,  small  plants,  etc.,  and  then  to  tell  what  can  be 
done  with  the  wood  and  plants,  that  cannot  be  done 
with  stone,  iron,  etc.  Also  lead  them  to  consider  whether 
both  of  these  classes  of  substances  are  obtained  from 
the  same  source,  and  whether  the  iron  and  stone  grow 
as  the  wood  and  small  plants  do.  When  the  most  ob- 
vious differences  between  these  two  classes  of  substan- 
ces have  been  perceived  by  the  pupils,  give  the  term 
Mineral  as  the  name  for  one  class,  and  Vegetable  as  the 
name  for  the  other. 

Second  Step. — The  teacher  may  next  call  attention  to 
the  three  great  classes  of  substances — mineral,  vegeta- 
ble, and  animal — and  lead  the  pupils  to  observe,  and  to 
tell  what  animals  and  vegetables  can  do  (as  take  food, 
breathe,  grow,  die),  which  minerals  cannot  do. 

Third  Step. — Let  the  pupils  be  led  to  notice  what 
animals  generally  can  do  which  vegetables  generally  can- 
not do  (as  move  from  place  to  place  by  their  own  pow- 
er) ;  also  to  observe  the  differences  between  the  food  of 
plants  and  that  of  animals ;  as  that  plants  feed  on  min- 
erals, or  simple  substances  from  the  earth  and  air,  while 
animals  feed  on  vegetables  and  other  animals. 

The  pupils  might  also  be  taught  that  substances 
which  once  formed  a  part  of  an  animal,  as  wool,  hair, 
bone,  skin,  are  called  animal  substances;  that  wood, 


OS  HOW  TO  TEACH 

bark,  gum,  sugar,  that  once  formed  a  part  of  a  vegeta- 
ble, are  called  vegetable  substances. 

Occupations. — The  exercises  on  this  topic  should 
not  only  lead  the  pupils  to  observe  and  describe  com- 
mon productions,  and  manufactured  articles,  but  should 
also  lead  them  to  consider  the  necessity  for  buying  and 
selling  productions  and  articles  of  manufacture ;  also 
how  these  are  taken  from  those  who  raise  or  make  them 
to  those  who  want  to  use  them. 


GEOGRAPHY. 

First  Step. — Review  the  Points  of  Compass,  in  train- 
ing the  pupils,  until  they  are  able  to  name  any  direc- 
tion, as  the  teacher  points,  and  to  point  in  any  direction 
named. 

In  connection  with  and  following  the  instruction 
relative  to  the  points  of  compass,  lead  the  pupils  to 
learn  the  location,  and  the  direction  from  the  school  of 
other  streets  near  the  school;  also  of  prominent  build- 
ings, as  churches,  post-office,  hotel,  railroad  depot, 
etc. ;  or  of  villages,  lakes,  farms,  groves,  forest,  streams, 
etc.,  within  the  range  of  the  children's  observation. 
The  teacher  should  represent  on  the  blackboard  the 
situation  of  the  school-house,  and  the  location  and  direc- 
tion from  it  of  the  places  mentioned,  and  allow  the 
pupils  to  copy  the  same  on  their  slates. 

Second  Step. — While  teaching  the  definitions  relative 
to  the  forms  of  land  and  water,  present  first  the  picture, 
or  a  drawing  upon  the  blackboard,  of  the  object  under 
consideration,  as  of  an  island,  peninsula,  cape,  strait, 


GEOGRAPHY.  99 

lake,  bay,  river,  etc. ;  then  show  how  the  same  or  a 
similar  object  is  represented  on  a  map.  Follow  this 
with  a  definition  to  be  learned  by  the  pupils.  As  the 
characteristics  of  each  form  of  land  or  water — as  that 
an  island  is  land  entirely  surrounded  by  water — is 
learned,  require  the  pupils  to  point  out  on  a  map  several 
representations  of  islands,  omitting  the  names  of  the 
particular  islands  in  this  stage.  Proceed  in  a  similar 
way  to  teach  all  the  definitions. 

Geographical  Cards,  containing  pictorial  and  map 
representations,  will  be  found  of  great  assistance  in 
illustrating  these  definitions. 

During  this  step  the  instruction  has  for  its  chief 
object  training  children  to  recognize  the  various  forms 
of  land  and  water,  by  means  of  their  characteristic 
features,  and  to  describe  each  by  suitable  definitions; 
hence  the  attention  of  pupils  need  not  be  directed  to 
the  names  and  location  of  particular  islands,  isthmuses, 
straits,  bays,  etc.,  at  this  time. 

Third  Step. — Commence  the  instruction  relative  to 
the  names  and  location  of  particular  places  with  the 
town,  village,  or  city  in  which  the  school  is  situated, 
and  extend  it  to  other  places  in  its  vicinity.  No  fixed 
limit  to  the  extent  of  this  exercise  can  be  given,  since 
the  length  to  which  it  can  be  profitably  carried  will 
depend,  in  pome  degree,  upon  the  personal  knowledge 
of  the  members  of  the  class  relative  to  these  places. 
The  teacher  should  aim,  however,  so  to  use  the  knowl- 
edge of  those  pupils  whose  personal  visitations  have 
made  them  acquainted  with  the  locations  of  the  great- 
est number  of  places,  as  to  extend  the  knowledge  of 
the  other  pupils. 


100  HOW  TO  TEACH 

Such  attention  should  be  given  to  the  location  upon 
a  map  of  the  town,  village,  or  city  in  which  the  school 
is  situated,  and  to  the  relative  location  and  direction 
from  it  of  the  chief  places  in  its  vicinity,  that  the 
pupils  will  be  able  to  point  them  out  on  an  outline 
map.  The  name  of  the  town,  village,  or  city,  of  the 
county,  and  of  the  State  in  which  the  pupils  live,  should 
be  taught,  and  their  location  shown  on  a  map. 

Fourth  Step. — In  teaching  the  shape  of  the  earth  by 
means  of  a  globe,  lead  the  pupils  to  compare  a  marble 
with  an  orange,  and  both  the  marble  and  orange  with 
a  globe,  and  thus  to  notice  that  each  one  resembles  the 
other  in  shape  only;  also  that  each  differs  from  the 
other  in  size.  By  this  means  prepare  them  for  under- 
standing that  the  globe  represents  the  earth  only  in 
shape.  Follow  this  with  some  simple  illustrations  as  to 
the  comparative  size  of  the  earth. 

Next  lead  the  pupils  to  compare  the  outline  forms  of 
the  grand  divisions  of  land,  water,  and  of  islands,  etc., 
represented  on  the  globe,  with  their  corresponding  repre- 
sentations upon  hemisphere  maps. 

Fifth  Step. — Talk  with  the  pupils  about  people  of 
different  races  and  nations,  and  point  out  on  the  globe, 
also  on  outline  maps,  the  location  of  the  countries  where 
each  may  be  found :  as  Africa,  the  home  of  the  colored 
men;  China,  the  home  of  the  Chinamen ;  Germany,  the 
home  of  Germans,  etc.  Proceed  in  a  similar  manner 
with  the  most  familiar  animals,  and  the  most  common 
productions  of  different  countries.  Give  the  name  of 
the  country,  and  show  its  location  on  a  globe,  also  on 
an  outline  map.  Point  out  Greenland  as  the  home  of 
the  white  bear ;  Africa  as  the  home  of  the  lion,  zebra,, 


GEOGRAPHY.  101 

ostrich  and  camel ;  Australia  as  the  home  of  the  kan- 
garoo; Spain  as  the  country  where  cork  and  raisins  are 
produced ;  South  America  as  the  country  from  which 
brazil-nuts  and  cocoa-nuts  are  obtained ;  West  Indies 
as  the  place  from  whence  we  obtain  oranges  and  bana- 
nas, etc. 

By  means  similar  to  that  herein  described  the  pupils 
may  be  made  to  realize  that  Geography  teaches  them 
about  the  homes  of  the  different  people,  animals,  and 
productions  which  they  have  seen,  and  of  which  they 
have  heard. 

The  aim  of  the  teacher  should  be  to  give  the  pupils  a 
good,  general  idea  of  the  shape  of  the  Earth,  of  the 
different  portions  of  it  as  the  homes  of  races  of  men, 
also  as  the  places  where  particular  fruits  grow;  and  of 
some  parts  as  having  continuous  Cold  weather,  and 
others  continuous  warm  weather.  This  object  must  be 
accomplished  chiefly  by  oral  instruction.  However,  the 
work  may  be  facilitated  by  placing  in  the  hands  of  the 
pupils  suitable  text-books  on  Geography,  to  be  exam- 
ined by  the  children  after  the  lesson  has  been. given 
orally  by  the  teacher  ;  but  in  no  case  should  the  pupils 
in  this  grade  be  required  to  study  a  lesson  in  the  book 
before  the  subject  of  it  has  been  presented  orally  by  the 
teacher,  as  above  indicated. 

Each  lesson  may  be  gone  over  a  second  time  by  the 
teacher,  after  the  pupils  have  studied  the  subject  in 
their  books.  The  order  of  the  lessons,  the  topics  pre- 
sented, and  the  general  character  of  the  facts  taught 
should  conform  to  the  directions  given  here,  without 
regard  to  the  order  of  presentation  in  the  text-books  in 
common  use. 

After  completing  the  course  of  objective  instruction 
in  Geography,  as  indicated  in  the  preceding  steps,  the 


102  HOW  TO  TEACH. 

pupils  will  be  prepared  to  commence  the  study  of  this 
subject  in  an  intelligent  manner  from  good  text- 
books. 

DRAWING  AND  WRITING. 

The  exercises  in  Drawing  and  Writing  for  the  Sixth 
Grade  may  be  continued  in  a  manner  similar  to  those 
of  the  Seventh  Grade.  Pupils  should  not  be  simply 
allowed  to  write,  they  should  be  taught  and  trained  how 
to  write  by  the  teacher.  Children  need  something 
besides  copy-books,  to  become  good  writers. 


GENERAL   SUGGESTIONS. 

Reviews. — Such  a  review  of  the  previous  lesson,  as 
an  introduction  to,  and  in  connection  with,  each  new  les- 
son of  the  same  subject,  should  be  had  as  will  cause  the 
pupils  properly  to  associate  together  the  important  facts 
previously  learned  with  those  of  the  new  lesson. 

General  reviews  of  subjects  should  be  had  at  least 
once  during  each  month.  On  these  occasions  the  lead- 
ing facts  learned  in  previous  grades,  upon  that  subject, 
should  be  included.  These  remarks  are  intended  espe- 
cially for  the  first  ft  ve  grades  of  this  course  of  instruc- 
tion. 

Progress  of  Classes. — Whenever  it  is  found  that 
a  class  has  advanced  further  in  one  or  two  subjects  of  its 
grade  than  it  has  in  others,  the  teacher  should  devote 
less  time  to  the  subject  in  which  the  class  has  thus 
advanced,  and  give  more  time  to  the  subjects  in  which 
the  class  has  made  the  least  progress.  By  this  means 
the  grade  of  the  class  may  be  equalized  in  all  its  studies. 


GENERAL  SUGGESTIONS.  103 

No  study  of  a  succeeding  grade  should  be  introduced 
into  a  class  of  a  lower  grade  before  that  class  has  com- 
pleted the  requirements  of  the  grade  in  all  its  studies. 

Time  Given  to  Each  Subject.— The  pupils 
belonging  to  the  first  five  grades  of  this  course  should 
not  spend  more  than  forty  minutes,  at  one  time,  upon 
the  same  subject.  And  in  the  first  two  grades  they 
should  not  spend  more  than  twenty  minutes  upon  the 
same  subject  at  one  time. 

The  mind,  as  well  as  the  body,  needs  rest.  Both  a 
change  of  subject,  and  a  change  in  the  manner  of  con- 
ducting class  exercises,  are  necessary  to  furnish  the 
opportunities  for  needed  rest  during  school  hours,  be- 
sides the  usual  recesses  of  school. 

Vocal  Music. — Instruction  in  vocal  music  ought  to 
be  given  to  the  pupils  of  all  the  grades  in  every  school. 

Principles  of  Education  Applied. — Teach- 
ers who  learn  to  apply  principles  of  Education  in  the 
order  of  presenting  knowledge,  and  in  their  methods  of 
teaching,  will  rarely  fail  of  becoming  successful  in  their 
work.  They  will  early  acquire  the  ability  to  determine 
for  themselves  how  to  commence  the  instruction  of  any 
class  under  any  conditions,  and  to  proceed  surely  step 
by  step  toward  the  end  in  view.  The  following  hints 
are  given  as  suggestions  to  young  teachers  who  desire 
to  attain  this  ability. 

Principle. — Commence  instruction  in  each  subject 
with  that  which  the  pupils  already  know  concerning  it, 
or  with  something  known  which  is  nearly  related  to  it, 
and  proceed  to  the  kindred  unknown  which  forms  the 
subject  of  the  lesson. 


104  HOW  TO  TEACH. 

To  ascertain  the  known,  or  the  related  unknown,  the 
teacher  must  consider  what  previous  opportunities  the 
children  have  had  for  obtaining  knowledge  of  the  sub- 
ject, and  then  by  questions  determine  the  true  attain- 
ments of  the  pupils  relative  to  the  matter  for  the  pro- 
posed lesson.  The  next  point  for  the  teacher  to  decide 
is,  how  can  that  which  the  pupils  already  know,  con- 
cerning the  subject  of  the  lesson,  be  used  in  the  best 
manner  to  aid  them  in  learning  that  which  they  do  not 
yet  know  of  it.  For  illustration,  let  this  principle  be  ap- 
plied to  teaching  Reading  to  a  class  of  young  children 
that  have  just  commenced  going  to  school. 

What  is  the  known  to  these  children,  which  relates 
to  reading?  [See  page  23.] 

What  is  the  unknown  to  be  first  taught  as  reading? 
[See  page  23.] 

How  can  the  known  be  used  to  aid  in  teaching  the 
unknown,  which  should  form  the  lesson  for  this  stage 
of  the  instruction  ?  [See  pages  23,  24,  25.] 

Suppose  a  class  has  made  sufficient  progress  in  learning 
to  read  to  be  ready  to  commence  using  the  first  reading 
book.  What  then  would  constitute  the  unknown  which 
should  be  taught  first?  [See  page  39.] 

How,  subsequently,  may  the  known  be  used  for  teach- 
ing that  unknown  which  forms  the  main  object  of  the 
lesson  ?  [See  pages  39,  40.  ] 

After  this  manner  the  subjects  of  instruction  should 
be  examined  by  the*  teacher,  in  each  of  the  grades; 
and,  as  a  most  important  part  of  the  process  of  teach- 
ing, the  main  points  of  each  preceding  lesson  should 
be  reviewed,  before  proceeding  with  the  new  matter,  as 
a  means  of  connecting  the  instruction  of  successive 
lessons  so  as  to  make  the  knowledge  acquired  a  complete 
whole,  so  far  as  it  extends. 


FIFTH    GEADE 

(LOWEST  GRAMMAR  SCHOOL.) 

Time  allowed,  about  five  montJis. 

OUTLINE   COURSE. 


LANGUAGE. 

Reading. — Of  the  grade  of  a  Third  Reader  (first  half),  with 
a  review  of  punctuation,  Roman  numbers,  and  elementary 
sounds;  and  with  exercises  on  the  subject-matter  of  tue  les- 
sons. 

Spelling* — From  the  reading  lessons,  with  miscellaneous 
words,  and  words  derived  therefrom;  also  exercises  in  writing 
words  and  short  sentences  from  dictation.  Particular  attention 
to  be  given  to  the  use  of  capitals. 

Definitions. — From  the  reading  lessons,  to  teach  the  mean- 
ing of  the  words,  with  illustrations  by  forming  sentences  ;  in  no 
case  to  be  committed  to  memory  and  mechanically  recited. 

Grammar. — Correction  of  Language. 


ARITHMETIC. 

Mental  Arithmetic. — As  far  as  in  written  arithmetic,  to 
include  exercises  in  the  analysis  of  operations  and  examples, 
and  in  rapid  calculation  without  analysis. 

Written  Arithmetic. — Through  the  simple  rules  and  Fede- 
ral money,  with  practical  examples. 

Tables  of  weights,  measures,  etc.,  completed  and  reviewed, 
with  practical  illustrations  and  simple  applications. 


106  HOW  TO  TEACH 


GEOGRAPHY. 

First  Stage. — Simplest  elementary  and  systematic  general  out- 
line of  the  geography  of  the  world  as  a  whole,  with  definitions 
and  illustrations  by  means  of  the  globe,  of  the  form,  magnitude, 
motions  of  the  earth,  zones,  latitude,  longitude,  etc. 

Second  Stage.— Outlines  of  North  America  and  the  West  In- 
dies, including  local  and  descriptive  geography. 


ELEMENTARY  SCIENCE. 

Food,  Clothing,  and  Building  Materials— Zoology. 

— By  oral  instruction,  to  develop  the  powers  of  observation  and 
reflection,  and  to  cultivate  facility  in  oral  description. 


DRAWING   AND  WRITING. 
On  Slates. — Continued. 

On  Paper. — Writing  in  books,  with  particular  attention  to 
position,  holding  pen,  etc.,  etc.,  as  in  Sixth  Grade. 

1.  Words    containing    easy  combinations ;    as   man,  name, 
noon,  soon,  etc. 

2.  Words  containing  long  and  short  letters ;  as  heart,  long, 
youth,  etc. 

3.  Words  with  easy  capitals ;  as  Ape,  Cold,  Ink,  Lamb,  Time, 
Useful,  Vanquish,  etc. 


LANGUAGE.  107 

How  TO  TEACH 

SUBJECTS     OF     THE    FIFTH     GRADE. 


LANGUAGE. 

Heading. — In  teaching  reading  in  tins  grade  and 
in  the  two  or  three  others  immediately  succeeding,  the 
chief  difficulties  to  be  overcome  may  be  classed  under 
the  following  heads : 

First. — Hesitation  over,  or  the  miscalling  of  familiar 
words. 

This  arises  from  want  of  practice,  and  where  strongly 
marked  should  claim  the  chief  attention. 

Second. — Mispronunciation  of  recognized  words,  as 
stun  for  stone,  winder  for  window,  theater  for  theater, 
etc. 

Third. — New  words  of  which  the  meaning  and  pro- 
nunciation are  not  yet  known  to  the  pupil. 

New  and  difficult  words  should  be  carefully  pro- 
nounced, and,  if  necessary,  explained,  before  the  piece 
or  paragraph  is  read  by  the  pupils. 

Fourth. — Faulty  enunciation.  This  is  in  great  part 
a  physical  difficulty  arising  from  deficient  training  of 
the  vocal  organs  and  of  the  ear,  though  sometimes  the 
result  of  slight  malformation. 

Distinctness  of  articulation  and  the  avoidance  of  all 
improper  clipping  of  terminations,  and  of  the  omission 


108  110  W  TO  TEACH 

or  slurring  of  syllables,  should  receive  careful  and  con- 
stant attention. 

Lists  of  common  words  liable  to  be  mispronounced, 
such  as  length  and  strength,  should  be  made  by  the 
teacher,  and  the  class  exercised  upon  them.  The  ele- 
mentary sounds  and  their  more  difficult  combinations 
in  words  and  phrases  requiring  great  mobility  of  the 
vocal  organs,  and  especially  final  consonants,  should  re- 
ceive frequent  attention.  It  should  not  be  forgotten  that 
the  difficulty  here  is  chiefly  physical,  and  can  be  readily 
overcome  by  suitable  exercises.  To  show  a  class  the  im- 
portance of  mobility  of  the  muscles  of  the  lips,  let  the 
teacher  read  a  paragraph  with  the  lips  almost  motion- 
less, and  then  read  it  again,  giving  as  much  play  as  pos- 
sible to  these  muscles.  The  great  contrast  in  distinct- 
ness of  articulation  will  be  at  once  manifest.  Among 
the  best  exercises  for  the  purpose  of  improving  the 
enunciation  are  the  well-known  "Three  gray  geese  and 
three  gray  ganders,"  "  She  sells  sea-shells."  "Saw  six 
slim  saplings,"  "Peter  Piper,"  "Theophilus  Thistle," 
"  Amidst  the  mists,"  etc.,  etc.  A  daily  exercise  of  five 
minutes  would  probably  be  sufficient  in  most  cases.  It 
should  be  very  spirited,  the  shorter  sentences  twice  or 
thrice  repeated,  and  with  the  greatest  rapidity  consist- 
ent with  perfect  distinctness. 

Particular  attention  should  be  given  to  pupils  of  for- 
eign birth  or  parentage,  so  as  to  insure  their  mastery 
of  the  principal  difficulties  of  English  pronunciation. 
Phonetic  drills  are  very  useful  for  this  purpose. 

Fifth. — Harsh  or  unnatural  tones.  The  voice  and 
manner  of  the  pupil  should  accord  with  the  character 
and  sentiment  of  the  selection.  All  draAvling,  sing-song 
tones  should  be  prevented.  This  is  easily  done  when 


LANGUAGE.  109 

the  pupils  are  led  to  understand  and  enter  into  the  spirit 
of  the  piece. 

In  the  employment  of  concert  exercises  in  reading, 
especial  care  should  be  taken  to  prevent  any  injury  to 
the  voice  by  harsh  or  unnatural  tones. 

Sixth. —  Vague  or  erroneous  conception  of  the  subject- 
matter  of  the  lesson  as  a  whole,  or  of  the  meaning  of 
particular  phrases,  sentences,  or  paragraphs. 

When  the  character  of  the  paragraph  or  of  the  les- 
son will  permit  it,  the  pupils  should  be  accustomed  to 
state,  in  their  own  language,  the  important  facts,  prin- 
ciples, and  moral  lessons  therein  taught.  Words,  phrases, 
or  allusions  should  be  briefly  explained,  whenever  neces- 
sary for  the  proper  understanding  of  the  piece  read. 

Seventh. —  Want  of  rhetorical  training.  Should  a 
large  number  of  consecutive  lessons  in  the  Reader  be 
of  the  same  general  character,  a  part  should  be  omitted, 
so  as  to  give  variety  of  style  and  subject.  No  selec- 
tion, other  than  the  best  English  poetry,  should  be  so 
long  dwelt  upon  and  so  frequently  repeated  as  to  ren- 
der the  exercise  a  mere  recitation. 

As  a  test  of  the  general  condition  of  the  reading, 
classes  should  occasionally  be  called  upon  to  read  un- 
familiar pieces  of  the  same  grade. 

Where  the  primary  object  of  the  exercise  is  to  teach 
elocution,  it  is  advisable,  quite  often,  to  require  all  the 
pupils,  except  the  one  reading,  to  close  their  books,  the 
teacher  also,  only  using  the  book  for  occasional  refer- 
ence. In  this  way,  both  the  teacher  and  the  class  will 
be  better  able  to  criticise,  and  the  criticism  will  be  more 
just  and  valuable.  Besides,  the  pupils  will  all  be  kept 
on  the  alert  to  listen,  and  the  one  reading  will  unavoid- 


no  now  TO  TEA cn 

ably  endeavor  to  pronounce  correctly,  enunciate  dis- 
tinctly, and  emphasize  naturally.  Additional  effect 
will  be  given  to  the  exercise  by  requiring  the  pupils  to 
reproduce,  in  their  own  language,  the  substance  of  what 
is  read  to  them. 

Where  a  simple  system  of  diacritical  marks  is  used 
in  the  Eeading  Book,  the  pupils  should  be  taught  to 
understand  and  apply  them.  An  occasional  brief  re- 
view of  the  Roman  numbers,  and  of  the  names  and 
signification  of  the  marks  used  in  punctuation,  should 
be  required. 

The  successful  application  of  these  suggestions  in- 
volves the  necessity  of  carefully  grading  the  exercises 
and  selections,  so  that  the  pupils  be  not  required  to 
read  pieces  which  are  above  their  comprehension.  This 
is  a  point  of  the  greatest  importance. 


SPELLING. 

THE  exercises  in  spelling  should  be  both  oral  and 
written,  but  principally  written. 

The  selections  of  words  from  the  reading  lessons 
should  be  so  made  that  the  class  will  not  be  prevented 
from  advancing  from  one  reading  lesson  to  another 
with  proper  rapidity.  When  a  Spelling  Book  is  used,  it 
should  be  made  an  auxiliary  to  the  Reader,  and  not  a 
substitute  for  it.  If  the  lists  of  the  Speller  contain 
unusual  words,  these  should  be  deferred  until  higher 
grades  are  reached.  No  time  should  be  spent  in  spell- 
ing words  which  the  pupil  does  not  understand. 

For  purposes  of  review,  teachers  should  keep  lists  of 
those  words  of  the  lessons  in  which  a  large  number  of 
mistakes  are  made  by  the  pupils. 


SPELLING.  HI 

In  oral  spelling,  care  should  be  taken  to  name  each 
letter  distinctly,  except  in  the  case  of  the  "doubles," 
which  are  to  be  distinctly  pronounced  as  such,  and  not 
as  "  d'blee  "  for  «  dotible-e,"  "  d'blow  "  for  «  double-o,"  etc. 

"Miscellaneous  words"  should  include  the  ordinary 
proper  names  of  persons  (not  the  surnames),  words 
naturally  suggested  by  those  of  the  reading  lessons,  and 
common  words  of  the  daily  life  of  the  household,  the 
shop,  and  the  street.  The  derivatives  required  should 
be  those  and  those  only  which  are  in  the  commonest 
conversational  use.  They  may  be  readily  obtained  by 
calling  upon  the  class  to  suggest  them.  The  modifica- 
tions of  the  primitives  required  in  order  to  form  them 
should  be  taught. 

The  written  exercises  should  be  as  neat  as  possible, 
care  being  taken  to  train  pupils  to  habits  of  orderly 
arrangement  of  their  work.  When  sentences  are  given, 
particular  attention  should  be  paid  to  the  ordinary 
troublesome  monosyllables,  to  the  proper  use  of  cap- 
itals, the  sign  of  the  possessive  case,  the  period,  the  in- 
terrogation mark,  and  the  use  of  the  hyphen  in  a  word 
divided  at  the  end  of  a  line. 


DEFINITIONS. 

In  selecting  words  for  definition,  two  leading  pur- 
poses should  be  specially  kept  in  view :  1.  To  impress 
or  illustrate  the  particular  meaning  of  the  word  as  used 
in  the  lesson ;  2.  To  enlarge  and  correct  the  pupil's 
own  vocabulary. 

Very  simple  words,  such  as  father,  water,  knife,  knee, 
look,  child,  etc.,  the  meaning  of  which  every  child  already 
understands,  should  not,  in  the  lower  grades  at  least, 


112  110 W  TO  TEACH 

be  assigned  for  definition.  Properly  to  define  such 
words  requires  a  nice  discrimination  in  the  use  of  lan- 
guage and  a  minuteness  of  analysis  beyond  the  power 
of  a  young  child.  Teachers  are  apt  to  go  astray  in  this 
direction.  It  is  principally  on  this  account  that  the 
limitation,  "  to  teach  the  meaning  of  the  words,"  has 
been  introduced  in  prescribing  this  part  of  the  grade. 
The  written  exercises  will  necessarily  contain  many 
such  words,  and  thus  the  child  will  learn  to  spell  them. 

"Where  a  word  has,  in  common  use,  two  or  more 
meanings  quite  diverse,  a  separate  oral  illustration 
should  be  required  for  each  ;  and  where  several  words 
differently  spelled  have  the  same  or  a  similar  pronuncia- 
tion, a  separate  construction  should  be  required  for 
each  in  the  written  exercises. 

Defining  one  part  of  speech  by  giving  another  part 
of  speech  as  a  synonym,  is  a  common  error.  It  may  be 
corrected  or  avoided  by  giving  small  groups  of  words, 
each  consisting  of  a  primitive  and  some  of  its  most 
commonly  used  derivatives,  and  requiring,  as  an  oral 
exercise,  a  phrase  or  a  sentence  to  illustrate  the  use  of 
each  word  in  the  group. 

Teachers  should  be  particularly  careful  to  comply 
with  the  direction,  "  in  no  case  to  be  committed  to 
memory  and  mechanically  recited."  The  mere  com- 
mitting of  dictionary  definitions  to  memory,  or  the  sub- 
stitution for  the  word  to  be  defined  of  another  word, 
perhaps  more  difficult  and  unusual,  is  a  perversion  of 
the  exercise.  It  is  not  only  useless  but  pernicious,  for 
it  neither  aids  in  mental  development  nor  adds  to  the 
pupil's  information,  nor  does  it  benefit  him  in  his  use 
of  language.  For  this  reason,  the  lists  of  words  given 
in  a  spelling  book  for  the  purpose  of  teaching  spelling 
are  not  well  adapted  for  teaching  the  meanings  of 


ARITHMETIC.  113 

words,  these  being  most  clearly  comprehended  when 
the  words  are  put  into  sentences  or  phrases. 

At  this  stage  of  the  pupil's  advancement,  a  full  exer- 
cise on  a  given  word  should  comprise  the  following: 
1.  Pronounce  it;  2.  Use  it  in  the  construction  of  a 
phrase  or  a  sentence;  3.  Define  it ;  4.  Write  a  sentence 
containing  it.  [For  the  whole  class.] 

In  the  performance  of  the  written  exercises  required 
for  definitions  in  this  grade,  the  pupils  may  not  only  be 
taught  the  meaning  of  the  words,  but,  by  a  skillful 
application  on  the  part  of  the  teacher,  bs  prepared  for 
the  exercises  in  composition  subsequently  prescribed. 
This  point  should  be  kept  in  view.  Correctness  in  the 
use  of  words,  propriety  in  the  thought,  the  accurate  use 
of  capitals,  punctuation  marks,  etc.,  should  be  invari- 
ably insisted  upon. 

ARITHMETIC. 

Mental  Arithmetic.  —  The  mental  arithmetic 
should  both  precede  and  accompany  the  written  arith- 
metic, step  by  step.  The  principal  distinction  between 
these  two  divisions  of  the  subject  is,  that  when  the 
numbers  involved  are  too  great  or  too  many  to  be  readily 
retained  in  the  memory,  the  slate  should  be  employed 
as  an  assistant. 

"Exercises  in  rapid  calculation  without  analysis" 
should,  as  far  as  possible,  be  of  the  most  practical 
character.  Examples  given  should  be  silently  wrought 
by  the  whole  class  simultaneously  as  in  written  arith- 
metic, and  the  results  obtained  be  written  upon  the 
slates,  promptly,  and  at  a  given  signal.  The  analysis 
can  then  be  separately  required  of  as  many  pupils  as 
may  seem  expedient 


1  U  HOW  TO  TEACH 

Illustration. — One  method  of  conducting  such  an 
exercise  is  subjoined.  Teachers  fertile  in  expedients 
will  devise  others  equally  good,  and  involving  the  follow- 
ing important  elements:  1.  The  exercise  to  be  simul- 
taneous; 2.  Silent;  3.  Spirited  throughout;  4.  All 
copying,  or  wrongly  claiming  the  answer  prevented. 
The  detail  may  be  greatly  varied : 

1.  Pupils  sit  silent  and  erect;  slates  lying  on  desk,  01- 
held  vertically,  resting  on  the  knees,  the  hands  being  at 
the  upper  corners;  pencils  in  right  hands. 

2.  Teacher  gives  question  with  distinctness. 

3.  Pupils  work  silently,  remaining  in  position  until 
the  answer  is  found,  when  each  silently  raises  the  right 
hand,  or  stands. 

4.  When  sufficient  time  has  been  given,  teacher  says 

"Ready Write,"   with  a  pause  between  the  words. 

At  the  last  word  the  answer  is  instantly  written  in  large 
figures,  but  only  by  those  standing,  or  whose  hands  are 
up,  and  the  slates  instantly  turned  with  the  answer 
toward  the  teacher.      No  further  working  or  correction 
allowed.     These  movements  are  better  executed,  after  a 
little  practice,  by  using  four  light  taps  of  the  pencil, 
meaning,  "Ready,"  "  Write,"  "  As  you  were,"  "  Show." 

5.  Teacher  calls  upon  some  one  to  read  the  answer, 
usually  upon  one  whose  results  are  frequently  wrong. 
Those  claiming  the  same  stand  if  sitting,  or  raise  the 
hand  or  the  slate  if  already  standing,  the  answer  being 
still  turned  toward  the  teacher. 

G.  If  thought  desirable,  an  oral  analysis  may  now  be 
demanded  of  any  pupil,  Avhether  he  obtained  the  answer 
or  not. 

The  explanatory  or  analytic  statements  made  by  the 
pupil  should  be  of  the  simplest  and  most  direct  charac- 
ter consistent  with  clearness,  and  all  unnecessary  repe- 


ARITHMETIC.  115 

titions  of  formulae  be  carefully  avoided.  Where  this  is 
not  done,  the  principal  effort  of  the  pupil  is  to  recall  in 
due  order  the  set  form  of  words,  rather  than  to  form  the 
arithmetical  combinations  necessary  to  the  solution. 

Besides  simple  examples  in  the  four  fundamental 
rules  and  Federal  money,  very  simple  operations  in- 
volving practical  applications  of  the  selected  tables  of 
money,  weight,  and  measure,  should  constitute  a  por- 
tion of  the  exercises  in  mental  arithmetic. 

In  the  explanation  or  analysis  of  examples  in  mental 
as  well  as  written  arithmetic,  the  pupils  should  gener- 
ally be  called  upon,  before  solving,  to  state  the  question. 

Mental  exercises  in  arithmetic  should  be  conducted 
in  a  spirited  manner.  They  should  always  have  the 
character  of  extemporized  exercises,  and  in  no  case 
form  a  part  of  the  home-work  of  the  pupil. 

Written  Arithmetic. — The  slates  should  be  kept 
in  the  best  condition  as  to  cleanness;  the  figures  should 
be  distinctly  and  neatly  made,  and  written  in  lines  par- 
allel to  the  upper  edge  of  the  slate.  A  reasonable  allow- 
ance should  be  made  for  imperfections  in  the  forms  of 
figures  in  those  exercises  where  haste  is  required;  yet 
every  effort  should  be  made  to  fix  in  the  pupils  habits 
of  care,  neatness,  and  system  in  all  that  pertains  to  the 
written  exercises. 

Exercises  in  adding  columns  of  figures  should  be  given 
with  such  frequency  as  may  be  found  necessary  to  pro- 
duce and  retain  accuracy  and  rapidity.  They  should  be 
in  both  forms — the  silent  and  the  oral. 

Every  form  of  counting,  whether  by  fingers,  dots, 
marks,  or  other  devices,  should  be  strictly  prohibited, 
and  the  class  should  be  frequently  tested  for  this  special 
purpose. 


11G  HOW  TO  TEACH 

The  pupil  should  be  allowed  to  name  only  the  succes- 
sive results  arising  from  the  addition  of  the  several 
successive  figures,  avoiding  all  that  oral  or  mental  repe- 
tition of  the  tables  which  is  known  as  the  "  spelling 
process,"  and  all  other  unnecessary  formulae. 

Illustration. 

789 
457 
633 

178 

Correct  Method.— %,  10, 17,  20  ;  0,  12,  17,  25,  etc.,  etc. 

Incorrect  Method. — 8  and  2  are  10, 10  and  7  are  17, 
17  and  9  are  26,  set  down  the  G  and  carry  the  2,  etc.,  etc. 
When  this  method  is  once  fixed,  it  is  difficult  to  change 
it.  It  acts  as  a  clog  to  the  mental  activity  of  the  pupil, 
who  finds  himself  unable  to  think  out  the  result  in  any 
other  way.  It  is  as  if  he  should  spell  aloud  every  word 
as  he  reads. 

The  above  remark,  in  regard  to  the  oral  or  mental  re- 
petition of  the  tables,  applies  to  all  the  fundamental 
rules  and  their  applications.  The  processes  should  be 
reduced  to  the  most  concise  form  practicable. 

"When  pupils  show  an  ability  to  add  in  two  or  more 
figures  at  a  time,  they  should  be  encouraged  to  do  so  in 
exercises  that  are  wrought  out  silently. 

When  the  divisor  is  less  than  13,  the  long-division 
process  is  not  to  be  employed  or  allowed. 

Short  practical  examples,  involving  two  or  more  of 
the  rules,  should  frequently  be  given,  and  in  such  a 
way  as  to  cultivate  the  intelligence  of  the  pupil. 

Examples  requiring  a  very  large  number  of  figures 


A  lUTHMKTIC.  117 

for  their  solution  Should  be  avoided,  except  as  far  as 
they  may  be  necessary  in  order  to  give  practical  expert- 
ness. 

Examples  should  be  given  to  test  the  pupils'  accuracy 
iii  writing  numbers  requiring  O's,  and  their  knowledge 
of  the  proper  methods  where  the  multiplier  or  divisor 
contains  O's. 

Exercises  should  be  given  to  insure  facility  in  read- 
ing and  writing  Federal  money,  and  in  reducing,  by  in- 
spection and  without  analysis,  dollars,  or  dollars  and 
cents,  to  cents  or  to  mills,  etc.,  etc.,  and  conversely. 
This  reduction  becomes  important  in  certain  cases  in 
division  of  Federal  money.  (See  Analysis  B.) 

Analogous  exercises  in  Federal  money  should  be  sub- 
stituted for  those  in  the  simple  rules  referred  to  in  the 
preceding  sections,  as  soon  as  may  be  found  expedient. 

In  all  practical  examples,  instead  of  telling  pupils  to 
add,  subtract,  multiply,  or  divide,  give  the  question  in 
such  a  manner  as  to  oblige  them  to  exercise  their  own 
judgment  as  to  the  method  and  principle  to  be  em- 
ployed. 

No  detailed  analysis  is  necessary  in  addition  or  sub- 
traction. 

Give  short  examples  of  bills  of  purchase  or  sale  in- 
volving several  items,  and  similar  to  those  required  in 
daily  life.  Let  them  be  put  into  proper  form  on  the 
slate,  with  names  and  date,  and  occasionally  receipted, 
and  the  receipt  explained. 

The  following  examples  involve  the  points  upon  which  pupils 
are  most  apt  to  fail  in  the  arithmetic  of  this  grade.  They  are  so 
highly  important  lhat  a  drill  upon  a  series  of  similar  examples 
is  recommended.  No  pupil  should  be  allowed  to  proceed  fur- 
thcr  till  he  has  thoroughly  mastered  them. 

Write  30,003,050—700,500,001)1 


118  HOW  TO  TEACH 

Multiply  30850  by  307  ;  by  4070  ;  by  2009. 

Divide  732427  by  200 ;  by  40000,  etc —Should  of  course  only 
be  done  by  short  division. 

Divide  732427  by  100 ;  by  10000,  etc.— Should  only  be  done 
by  pointing  off. 

Write  3  dollars  and  5  cents  ;  10  dollars  and  7  cents,  etc. 

Bought  for  $2095.07,  sold  for  $2500.  How  much  did  I  gain  or 
Jose? 

Sold  320  bushels  for  $176.     How  much  a  bushel  ?    Analyze. 

Spent  $42  for  tea  at  87£  cents  a  Ib.  How  many  Ibs.  did  I 
buy  ?  Analyze. 

Spent  $8  for  coffee  at  40  cts.  a  Ib.  How  many  Ibs.  did  I  buy  ? 
Analyze. 

If  24  yards  cost  $20.40,  what  will  17  yards  cost  ?    Analyze. 

If  24  yards  cost  $20.40,  how  many  yards  can  be  bought  for 
$14.45?  Analyze. 

NOTE.— If  fractions  arise  in  the  first  stage  of  examples  similar  to  the  last 
two,  they  may  be  rejected  in  the  second  stage  in  this  grade. 

The  following  are  all  the  forms  of  arithmetical  analysis  neces- 
sary to  the  fifth  grade  : 


FORMS  OF  ARITHMETICAL  ANALYSIS 

FOR  BOTH  MENTAL  AND  WRITTEN  ARITHMETIC. 

A.  (  Fundamental) — Multiplication. 

Question. — If  one  yard  cost  $3,  what  will  4  yards  cost  ? 
Analysis. — If  one  yard  cost  $3,  4  yards  will  cost  4  times  $3, 
•which  are  $12. 

NOTE.— Avoid  the  too  concise  form,  "  will  cost  4  times  3,  which  are  12." 

B.  (Derived} — Division.    (1.) 

Question.— If  one  yard  cost  $3,  how  many  yards  may  be  bought 
for  $12  ? 

Analysis.— If  one  yard  cost  $3,  $12  will  buy  as  many  yards  as 
$3  are  contained  times  in  $12,  which  are  4  yards. 

NOTE.— Avoid  the  too  concise  form  "  as  many  as  3  are  contained  in  12." 

Question.— Spent  $42  for  tea,  at  87ic.  a  pound.  How  many 
pounds  did  I  buy  ? 


ARITHMETIC.  119 

Analysis. — $43  are  42000  mills,  and  87£  cents  are  875  mills.  I 
can  buy  as  many  pounds  as  875  mills  are  contained,  etc. 

See  preceding  "  Suggestions  "  for  remark  about  reducing  Federal  money 
without  analysis. 

C.  (Derived) — Division.     (2.) 

Question. — If  4  yards  cost  $12,  what  will  one  yard  cost  ? 
Analysis. — If  4  yards  cost  $12,  one  yard  will  cost  $  of  $12, 
which  is  $3. 

NOTE.— Avoid  the  very  faulty  forms  "as  much  as  4  is  contained  in  $12," 
or  "  times  in  $12,"  or  "  4  is  contained  in  12." 

Question.— If  5  Ibs.  cost  $3,  what  will  1  Ib.  cost  ? 
Analysis.— If  5  Ibs.  cost  $3  or  300  cents,  1  Ib.  will  cost  i  of  300 
cents,  which  is  60  cents. 

COMBINATIONS  OF  A,  B,  AND  C. 

Cand  A.    Division  and  Multiplication. 

Question. — If  4  yards  cost  $12,  what  will  9  yards  cost  ? 
Analysis. — First  by  C  for  price  of  1  yard,  then  by  A  for  price 
of  9  yards. 

C  and  B.    Division.    (2)  ami  (1). 

Question. — If  4  yards  cost  $12,  how  many  yards  may  be  bought 
for  $27? 

Analysis. — First  by  C  for  price  of  1  yard,  then  by  B  for  num- 
ber of  yards. 

NOTE  1.—  Avoid  set  forms  of  giving  questions.  Vary  the  order  of  statement 
as  far  as  is  consistent  with  perfect  clearness.  For  instance,  the  last  question 
might  have  been  put  thus:  Spent  $27  for  cloth.  How  many  yards  did  I  buy, 
if  $12  bought  3  yards;  or,  Ho\v  many  yards  for  $27,  if  4  yards  cost  $12? 
etc.,  etc. 

NOTE  2.— In  this  grade  avoid  examples  in  which  fractions  forma  part  of  the 
quotient. 

NOTE  3.— It  is  frequently  an  assistance  to  some  pupils  to  have  them  divide 
each  question  into  conditions  and  demand — as  in  C  and  A.  "  The  condition  is, 
that  4  yards  cost  $12.  The  demand  is,  what  is  the  price  of  9  yards."  Such 
devices  should  be  sparingly  used. 

NOTE  4.— Analysis  A  and  B  apply  to  questions  in  the  tables,  substituting 
the  word  since  for  if.  Examples  :  How  many  quarts  in  five  pecks  ?  Since  one 
peck  contains  eight  quarts,  flve  pecks  contain,  etc.,  etc.  How  many  feet  in 
84  inches?  Since  12  inches  make  1  foot,  84  inches  contain  as  many  feet,  etc., 
etc. 


110  W  TO  TEACH 


,      TABLES. 

In  this  grade,  the  tables  of  the  preceding  grade  should  be 
thoroughly  reviewed,  with  the  following  additions ; 

Time. — Teach  about  leap-year. 

Avoirdupois  Weight.— 7000  grains  =  1  pound ;  2240 
pounds  —  1  old  ton  ;  62|  pounds,  or  1000  ounces  =  1  cubic  foot 
of  water. 

Troy  Weight. — Explain  its  use,  the  great  difference  be- 
tween its  pound  and  ounce,  and  those  of  Avoirdupois  Weight,  the 
grain  being  the  only  identical  element.  24  grains  =  1  penny- 
weight ;  20  pennyweights  —  1  ounce  ;  12  ounces,  or  5760 
grains  =  Ipound. 

Apothecaries'  Weight. — Explain  its  use.  Show  that  it 
differs  from  Troy  Weight  in  nothing  but  the  method  of  subdivid- 
ing the  ounce.  Teach  that  the  fluid  ounce  is  a  measure,  and  not 
a  weight.  20 grains  =  1  scruple;  3  scruples  =  1  dram  ;  8  drams 
=  1  ounce ;  12  ounces  =  1  pound. 

Long  Measure. — Add  the  following :  Explain  the  use  of 
each  term.  4  inches  =  1  hand  ;  3  feet  —  1  pace  ;  6  feet  =  1 
fathom ;  1£  miles  =  1  knot. 

Surveyors'  Long  Measure. — 4  rods,  or  66  feet,  or  100 
links  =  1  chain  ;  80  chains  —  1  mile. 

Surveyors'  Square  Measure.—  Explain  the  local  use  of 
section  and  township.  16  square  rods  —  1  square  chain ;  10 
square  chains  =  1  acre  ;  640  acres  —  1  square  mile  or  section;  36 
square  miles  —  1  township. 

Solid  or  Cubic  Measure. — Explain  its  use,  and  the 
difference  in  kind  between  the  linear,  superficial,  and  solid  units  of 
the  same  name.  1728  cubic  inches  =  1  cubic  foot ;  9  cubic  feet  =  1 
cubic  yard  ;  128  cubic  feet  =  1  cord  of  wood  ;  2150  cubic  inches 
=  1  bushel ;  231  cubic  inches  =  1  gallon. 

singular  Measure. — Teach  the  following  terms  :  Circle, 


GEOGRAPHY.  121 

circumference,  quadrant,  radius,  diameter.  Teach  the  notation. 
Give  examples  in  reading,  as  16°  17'  45".  60''  =  1  minute; 
60'  =  1  degree  ;  90°  =  1  quadrant ;  360°  =  1  circle ;  360°  = 
circumf.  of  the  Earth ;  69£  miles  =  1  degree  of  latitude ;  cir- 
cumference of  a  circle  =  3f  times  the  diameter. 

English  Money,  etc. — The  usual  table.  Teach  the  value 
of  a  pound  sterling — $4.866£.  Teach  the  value  of  a  franc — 18 
cents  6  mills ;  also  of  the  mark  of  the  German  Empire — 23 
cents  8  mills. 

If  any  foreign  dollar  is  taught,  let  it  be  the  thaler  of  Germany 
— 71  cents  4  mills. 

GEOGRAPHY. 

General  Suggestions  for  all  Grades. — It 

is  of  the  first  importance  that  geography  should  be 
so  taught  and  reviewed,  as  not  to  leave  in  the  mind  of 
the  pupil  a  mere  collection  of  facts,  without  mutual  re- 
lation or  dependence.  On  the  contrary,  he  should, 
from  the  first,  be  led  to  consider  the  earth  as  man's 
dwelling-place — its  motions  as  bringing  him  the  neces- 
sary vicissitudes  of  day  and  night,  and  the  changes 
of  the  seasons — its  land-surface  as  the  chief  theater  of 
animal  and  vegetable  life — the  ocean  as  the  Avorld's  broad 
highway,  and  the  exhaustless  source  of  clouds  and  rains, 
so  necessary  to  every  form  of  life  on  the  laud-surface — 
the  great  permanent  air-currents  as  carrying  to  the 
land  this  moisture  from  the  sea — the  mountains  as  its 
condensers,  as  Avell  as  the  chief  source  of  mineral  wealth 
— the  springs  and.  rivers,  with  their  branches,  as  carry- 
ing back  again,  and  over  the  land,  the  ever-circulating 
water  of  the  ocean — and  of  cities  and  towns,  not  as  black 
dots  on  a  map,  in  colored  patches,  which  he  has  learned 
to  call  countries,  perhaps  near  some  crooked  black 
streaks  which  he  has  learned  to  call  rivers,  but  as  the 

6 


[22  HOW  TO  TEACH 

centers  of  social  life  and  development,  the  seats  of 
government,  and  the  crowded,  busy  hives  of  human  in- 
dustry and  intelligence. 

When  geography  is  thus  taught,  it  is  one  of  the  most 
interesting,  important,  and  practical  of  studies;  but  if 
it  is  taught  chiefly  as  a  description,  by  unvarying  for- 
mulae, of  long  lists  of  rivers,  capes,  peninsulas,  bou  ndaries, 
etc.,  supplemented,  perhaps,  by  a  precise,  verbatim  repe- 
tition of  the  descriptive  geography,  as  contained  in 
even  the  very  best  text-book,  it  is  one  of  the  dullest  and 
most  unprofitable  of  studies. 

The  text-book  is  a  most  important,  and  even  indis- 
pensable auxiliary i  but  there  is  no  more  common  and 
pernicious  error,  than  that  of  substituting  it  in  place  of 
the  teacher,  who  thus  is  degraded  into  a  mere  stupid, 
profitless,  and  mechanical  hearer  of  lessons.  The  requi- 
sites for  successful  teaching  are  a  globe,  a  blackboard, 
an  outline  map  and  pointer,  and  a  good  text-book.  The 
pupil's  first  impressions  should  be  formed  from  the 
globe,  rather  than  from  the  flat  and  distorted  repre- 
sentation of  the  map.  When  the  text-book  is  to  be  used, 
and  important  and  comprehensive  lessons  given,  such 
as  the  presentation  of  the  general  outline  of  the  world 
as  a  whole,  or  of  a  continent  or  grand  division,  or  of  the 
United  States  as  a  whole,  the  subject  should  first  be  gone 
over  orally,  in  outline,  by  the  teacher.  If  this  be  done 
in  a  spirited  manner,  and  the  results  carefully  tested,  the 
detailed  study  of  the  text-book  will  be  greatly  assisted 
and  unified  by  the  comprehensive  view  thus  imparted, 
and  the  important  details  more  surely  remembered. 

Geography    of  the   Fifth   Grade.— hi  the 

preceding  grade,  the  pupil  has  been  taught  the  leading 
elementary  ideas  upon  which  geography  is  founded ;  in 


GEOGRAPHY.  123 

the  present  grade,  these  are  to  be  reviewed,  explained, 
and  systematized,  beginning  with  a  general  view  of  the 
world.  The  following  is  a  syllabus  of  the  points  which 
should  claim  attention : 

Syllabus  for  the  Fifth  Grade.  Part  1st.— The  form  of 
tfie  earth,  its  magnitude,  the  continents  and  grand  divisions,  their 
relative  positions,  their  connecting  isthmuses,  and  a  few  of  their 
most  important  projections — the  oceans,  their  positions,  and  prin- 
cipal arms  and  islands — five  or  six  of  the  great  mountain  systems 
of  America,  and  from  eight  to  ten  in  the  rest  of  the  world  ;  three  or 
four  well-known  volcanoes — about  a  dozen  each  of  the  chief  rivers 
and  straits,  and  about  half  as  many  great  lakes — from  ten  to  a 
dozen  of  the  most  important  cities  of  the  world,  and,  in  a  very 
general  way,  the  location  of  the  most  important  countries,  such 
as  the  United  Stales,  Great  Britain,  Germany,  Japan,  China,  etc. 
With  each  of  these  cities  and  countries  some  interesting  or  im- 
portant fact  should  be  at  once  associated. 

Part  2d.  (To  be  taught  as  facts,  in  the  simplest  outline,  and 
without  attempting  to  explain  according  to  any  of  the  hypothe- 
ses of  scientific  physical  geography,  using  the  map  and  globe, 
whenever  necessary,  to  impress  any  particular  statement  on  the 
pupils'  minds.)  A  brief  notice  of  the  ocean  currents,  their  direc- 
tion, temperature,  and  use,  pointing  out  only  the  equatorial  cur- 
rent, one  Arctic  current,  one  Antarctic  current,  and  the  Gulf 
stream — the  trade  winds  (very  briefly),  their  location,  direction, 
usei,n  commerce,  and  their  influence  (in  assisting  to  produce  the 
great  South  American  rivers,  the  Nile,  etc.) — a  general  notion  of 
climate,  as  affected  by  distance  from  the  equator,  and  by  eleva- 
tion— the  motions  of  the  earth,  and  the  inclination  of  its  axis — the 
zones,  their  limits,  and  a  very  few  of  their  well-known  and  char- 
acteristic plants  and  animals,  and,  in  a  very  general  way,  the 
location  of  the  chief  races  of  mankind. 

"  Outlines  of  North  America."— First :  Treat  the  con- 
tinent as  a  whole,  pointing  out  its  separate  countries,  most  im- 
portant capes,  peninsulas,  islands,  and  arms  of  the  sea;  its 
divisions  into  mountains,  plateaux,  and  lowland  plains,  naming 
only  a  few  of  the  most  important  of  each. 


124  SOW  TO  TEACH 

Iceland,  Greenland,  Alaska,  and  all  other  Arctic  Geography  to 
be  treaied  very  briefly,  and  chiefly  with  reference  to  climate,  re- 
sources, and  people. — Newfoundland;  the  Dominion  of  Canada,  its 
surface,  its  provinces  and  territories,  with  their  climate,  resources, 
and  people,  and  our  trade  with  them  ;  the  form  of  government ;  the 
capital  of  the  Dominion  and  those  of  the  provinces,  and  the  other 
most  important  towns ;  the  commercial  and  international  im- 
portance of  the  St.  Lawrence  River  and  the  Great  Lakes,  and  the 
small  importance  of  the  other  rivers,  of  which  three  or  four  will 
be  enough. 

United  States. — A  simple  outline  will  embrace  the  follow- 
ing : 

Local  Geography. — The  boundaries  of  the  country  as  a 
whole ;  its  dimensions  in  round  numbers ;  the  location  of  the  great 
mountain  systems ;  the  western  plateaux  'a  section  of  the  country 
roughly  drawn  in  chalk  upon  the  blackboard  will  be  found  effi- 
cient] ;  the  high  western  plain;  the  low  central  plain;  the  eastern 
slope,  and  the  California  basin  ;  about  a  dozen  of  the  chief  rivers, 
with  the  great  branches ;  about  five  or  six  each  of  the  great 
lakes,  bays,  and  capes  ;  about  twenty  of  the  principal  cities. 

Descriptive  Geography  will  include  a  very  brief  descrip- 
tion of  the  highlands,  lowlands,  and  drainage  system  already- 
pointed  out ;  the  climate  and  its  gradual  modifications  by  lati- 
tude, elevation,  and  distance  from  the  sea ;  and  a  general  state- 
ment of  the  leading  agricultural  staples  in  the  order  of  their 
latitude— rice,  sugar,  cotton,  tobacco,  corn,  and  wheat. 

Mexico. — Its  surface,  climate,  resources,  and  people ;  their 
language,  government,  and  social  condition  ;  about  five  or  six  of 
the  principal  cities. 

Central  America  very  briefly;  the  names  of  its  states  and 
their  capitals,  and  their  general  similarity  to  Mexico. 

West  Indies,  the  principal  groups,  about  ten  or  a  dozen  of 
the  most  important  islands ;  five  or  six  principal  ports  ;  the 
climate,  resources,  and  people :  their  colonial  relations,  and  their 
commerce  with  the  United  States,  if  important. 


LANGUAGE.  125 


LANGUAGE. 

Correction  of  Language. — In  all  the  grades 
the  pupils  should  be  trained  in  the  correction  of  lan- 
guage, and  taught  to  avoid  common  errors  of  speech. 
This  is  best  accomplished  in  connection  with  the  dicta- 
tion exercises  required  in  the  several  grades;  also  by  oral 
exercises  specially  adapted  to  this  purpose,  and  by  inci- 
dental instruction  during  the  recitations  and  lessons  in 
other  subjects,  as  in  the  definition  exercises,  the  lessons 
in  elementary  science,  etc.  Indeed,  every  exercise  in 
which  the  pupils  are  required  to  use  their  own  language, 
either  orally  or  in  writing,  should  be  made  a  vehicle  for 
this  instruction,  the  object  being  to  impart  the  habit  of 
using  correct  language.  It  is  of  the  greatest  importance 
that  this  habit  should  be  acquired  at  an  early  age,  for 
without  it,  the  technical  study  of  grammarwill  scarcely 
prove  adequate  to  impart  fluency  in  the  correct  use  of 
language.  The  old  habits,  in  spite  of  the  knowledge  of 
principles  and  rules,  will  be  always  apt  to  show  them- 
selves. 

On  this  account,  teachers  cannot  be  too  careful  them- 
selves in  the  use  of  language.  Their  words  as  well  as 
their  acts  shoiild  present  a  model  for  the  imitation  of 
their  pupils ;  and  example  in  this,  as  in  other  things, 
will  prove  far  more  potent  than  precept.  For  special 
exercises  in  this  department  of  the  instruction,  the  fol- 
lowing suggestions  are  made : 

Write  on  the  blackboard  such  faults  in  expression  as 
are  liable  to  be  committed,  including — 1.  Ungrammati- 
cal  expressions. :  as  /  haven't  no  book  ;  I  haven't  got  my 
pencil ;  I  seen  him  do  it,  etc.  2.  Slang :  This  is  an  awful 
easy  lesson,  etc.  The  faulty  expressions  written  in  this 


126  HOW  TOTE  AC U 

way  should,  however,  consist  of  such  as  may  have  been 
committed  by  some  of  the  pupils  of  the  class,  lest  those 
who  have  acquired  good  habits  of  speech  be  contami- 
nated by  having  their  attention  called  to  such  errors. 

Award  premium  marks,  or  some  other  kind  of  reward, 
to  those  who  succeed  in  pointing  out  improper  expres- 
sions on  the  part  of  their  classmates;  but  let  this  be 
done  in  the  right  spirit,  and  not  for  the  purpose  of 
subjecting  any  of  the  pupils  to  jeers  or  ridicule.  The 
fact  that  their  language  may  be  made  the  subject  of 
criticism  by  their  fellow-pupils,  will  put  all  on  the  alert 
to  use  the  best  modes  of  expression  in  their  power,  and 
then  correction  will  have  a  permanent  effect  in  improv- 
ing them  in  the  use  of  language. 

Sometimes  one  or  more  pupils  may  be  selected  by 
the  class  to  act  as  censors  for  a  definite  period  (say  a 
week),  and  to  call  attention  to  errors  made  by  any  of 
the  pupils  of  the  class.  The  object  of  this  and  the  pre- 
vious suggestion  is  to  make  the  pupils  critics  on  them- 
selves and  others,  most  of  the  inaccuracies  committed 
resulting  rather  from  carelessness  and  inattention  than 
from  a  want  of  knowledge.  The  teacher  will,  of  course, 
often  find  it  necessary  to  give  direct  instruction  in  rela- 
tion to  certain  expressions. 

Of  course,  no  instruction  in  technical  grammar,  or  in 
any  grammatical  rules,  is  required  until  the  next  grade. 


ELEMENTARY  SCIENCE. 

(By  Oral  Instruction.) 

GENERAL  SUGGESTIONS  FOR  ALL  GRADES. 

The  leading  object  in  this  branch  of  instruction  is  to 
cultivate  habits  of  observation  and  reflection,  and  to  give 


ELEMENTARY  SCIENCE.  107 

facility  in  oral  description.  Avoid  everything  tend- 
ing to  convert  these  lessons  into  recitations  of  set  forms 
of  words,  however  these  forms  may  have  been  obtained, 
however  well  they  may  be  understood  by  the  pupils,  and 
however  important  the  facts  thus  stated. 

" Familiar  objects"  and  familiar  animals,  plants,  and 
minerals  take  precedence  of  all  others  in  the  selection 
of  topics. 

It  is  neither  possible  nor  desirable  to  attempt  to  teach 
all,  or  even  the  greater  part  of  the  topics  that  might  be 
classified  with  the  requirements  of  any  grade.  No  topic 
should  be  treated  exhaustively,  nor  should  the  topics 
selected  be  so  few,  or  so  frequently  reviewed,  as  to  nar- 
row down  or  suspend  the  discipline  of  the  observing 
faculty.  The  selection  and  limitation  must  be  left  to 
the  good  sense  of  the  teacher. 

The  objective  method  of  teaching  presents  two  dis- 
tinct, though  intimately  related  departments.  Percep- 
tive teaching,  in  which  the  object,  as  an  acorn  or  an  egg, 
is  directly  presented  to  the  pupils'  senses ;  and  conceptive 
teaching,  in  which  impressions  previously  received  are 
recalled,  arranged,  and  utilized,  the  objects  themselves 
not  being  presented  to  the  senses  during  the  lesson. 
An  oak,  an  elephant,  or  a  thunder-storm,  would  fall 
under  the  latter  department. 

The  tise  of  pictures,  models,  or  other  sensible  repre- 
sentations of  objects,  constitutes  an  important  combina- 
tion and  modification  of  the  two  principal  methods, 
and  should  be  often  employed. 

Definitions  should  be  very  sparingly  introduced,  and 
never  in  the  first  stage  of  a  subject  If  given  at  all, 
they  should  sum  up  knowledge  already  attained.  The 
terms  organic,  inorganic,  vegetable,  animal,  and  mineral, 
are  prominent  among  the  very  few  terms  requiring  defi- 


J28  SOW  TO  TEACH 

nitiou.  Such  definitions  should  be  prepared  for  by  a 
process  at  once  inductive  and  objective. 

No  fact  which  the  teacher  can  readily  lead  the  pupil 
to  discover  for  himself,  should  be  imparted  by  the 
teacher.  Important  facts  not  readily  derived  from  the 
pupil's  own  observation,  must,  of  course,  be  supplied  by 
the  teacher.  Avoid  overloading  a  topic  by  details.  No 
topic  should  be  selected  in  which  the  number  of  facts 
to  be  told  bears  a  large  proportion  to  those  which  the 
pupil  may  be  led  to  discover  for  himself. 

The  language  used  by  the  pupil  should  be  entirely  his 
own,  excepting,  of  course,  the  few  indispensable  defini- 
tions. 

The  process  employed  will  present  two  distinct  stages: 
First,  the  analytical  or  preparatory,  in  which  the  teacher 
leads  the  pupil  by  questions  to  discover  or  to  remember 
the  properties  or  peculiarities  of  an  object,  or  to  state 
any  other  important  facts  associated  with  it.  The  re- 
sponses by  the  pupil  will  be,  of  course,  in  his  own  words ; 
and  the  additional  statements  which  the  teacher  him- 
self may  find  necessary  to  make,  will  be  given  in  the 
form  of  conversations.  This  stage  gives  the  principal 
discipline  of  the  powers  of  observation  and  reflection. 

The  points  thus  considered,  and  the  facts  thus  stated 
should  be  written  upon  the  blackboard  in  the  briefest 
possible  synoptical  form,  but  each  only  after  it  has  been 
considered.  While  some  such  synopsis  is  indispensable 
to  the  teacher  as  the  first  step  of  preparation  for  giving 
the  lesson,  it  should  never  be  presented  to  the  pupil  ex- 
cept by  the  gradual  process  above  indicated. 

The  second  or  review  stage  of  the  process  is  based  upon 
the  results  of  the  first,  and  furnishes  the  principal  dis- 
cipline of  the  powers  of  description  or  oral  statement. 
The  facts  already  considered  should  be  re-arranged,  if 


ELEMENTARY  SCIENCE.  129 

necessary,  into  an  orderly  synopsis  upon  the  black- 
board, the  pupils  being  called  upon  to  assist  in  this 
arrangement.  They  should  then  be  required,  in  turn, 
to  state  what  they  can  recall  of  each  item  of  the  synop- 
sis, then  of  each  group  of  items,  and,  lastly,  of  the  whole 
subject.  Then  the  synopsis  may  be  wholly  or  in  part 
removed  or  hidden,  and  the  oral  process  of  review  re- 
peated. As  a  final  stage,  and  before  dismissing  the  sub- 
ject, an  extempore  composition,  with  or  without  the  aid 
of  the  synopsis  upon  the  board,  should  be  written  by 
each  pupil  upon  his  slate. 

OUTLINES  OF  ZOOLOGY. 

In  relation  to  this  part  of  the  fifth  grade,  the  fol- 
lowing suggestions  are  made : 

Zoology  being  a  science  of  classification,  it  is  indis- 
pensably requisite  to  teach  the  distinctions  upon  which 
the  classification  depends. 

Only  the  simplest  outline  need  be  taught,  with  such 
facts  and  details  as  seem  most  naturally  appropriate  to 
illustrate  the  subject. 

The  process  of  classification  being  naturally  objective, 
that  is,  animals  being  classified  by  their  obvious  pecu- 
liarities, the  pupil  should  be  led,  by  an  exercise  of  the 
observing  faculties,  to  discover  the  leading  peculiarities 
himself. 

For  instance,  suppose  the  teacher  wishes  to  lead  to 
the  perception  of  the  basis  of  the  classification  into 
the  four  great  types  or  sub-kingdoms.  Write  upon  the 
blackboard  the  names  of  a  sufficient  number  of  fa- 
miliarly known  animals  without  classification.  If  he 
have  their  pictures  in  books,  or  on  charts,  let  each  be 
shown  before  asking  and  writing  its  name.  Let  the 

6* 


130  SOW  TO  TEACH 

pupils  spell  each  name  before  the  teacher  writes  it.  Sup- 
pose them  to  be  lobster,  ox,  oyster,  dog,  beetle,  starfish, 
snail,  and  coral.  Lead  the  pupils  to  see  and  decide  for 
themselves  which  two  or  three  most  resemble  each 
other.  Adroit  questioning,  and  a  little  patience,  will 
soon  make  them  group  together  the  lobster  and  the  beetle 
on  account  of  their  hard,  jointed  rings,  and  their  many 
equally  hard  limbs;  the  ox  and  the  dog,  from  their 
four  legs,  and  their  similarity  as  to  eyes,  ears,  and  other 
organs ;  and  the  oyster  and  the  snail,  from  their  hard 
shells  and  soft  bodies.  The  remaining  starfish  and  coral 
will  present  difficulties,  because  not  so  familiarly  known ; 
but  these  may  readily  be  overcome  by  the  use  of  pic- 
tures or  even  rough  sketches  on  the  board. 

Having  thus  grouped  the  names  upon  the  blackboard, 
a  few  questions  will  lead  to  the  perception  that  the  ani- 
mals of  one  group  have  a  backbone,  composed  of  many 
pieces,  and  an  internal  bony  skeleton  ;  those  of  another 
are  made  up  of  distinct  rings  and  joints';  and  so  on  of  the 
other  groups,  each  of  which  may  now  be  readily  ex- 
panded, by  asking  the  pupils  for  the  names  of  other  ani- 
mals, and  the  reasons  for  assigning  them  to  a  particular 
group. 

Then,  AND  NOT  TILL  THEN,  the  teacher  should  give 
and  explain  the  terms  vertebrate,  articulate,  etc.,  care- 
fully reviewing  and  questioning  the  class,  to  see  that  all 
is  understood. 

In  the  same  manner,  the  classes  of  the  vertebrates,  and 
the  principal  orders  of  the  mammalia,  etc.,  may  easily  be 
drawn  from  the  pupil's  own  observations  of  resem- 
blances and  differences. 

The  terms  mineral,  vegetable,  animal,  organic,  and  in- 
organic, should  be  previously  taught  or  reviewed  in  a 
similar  manner,  through  the  perceptions  of  the  pupil, 
guided  by  the  questions  of  the  teacher. 


ELEMENTARY  SCIENCE.  131 

Remember  that  the  skillful  use  of  interrogation  is 
the  teacher's  chief  means  of  awakening  thought,  and  pro- 
ducing lasting  impressions. 

Well-known  typical  animals  should  be  taken  as  the 
objective  basis  of  the  classification ;  such  as  man, 
monkey,  bat,  cat,  rat,  horse,  deer,  cow,  and  whale; — 
eagle,  parrot,  canary,  rooster,  ostrich,  snipe,  and  duck  ; — 
turtle,  alligator,  rattlesnake,  and/ro0r; — perch,  cod,  shark, 
etc. ; — bee,  butterfly,  beetle,  etc. ; — spider,  cray-fish,  and 
crab; — squid,  snail,  &nd  oyster  ; — starfish,  jellyfish,  and 
corals. 

The  simplest  names  should  be  used,  where  possible,  in 
preference  to  the  more  scientific,  or,  at  least,  as  pre- 
paratory thereto ;  thus,  it  is  better  to  use  the  term  four- 
handed  than  quadrumana ;  gnawers  than  rodentia; 
scratchers  than  rasores  ;  two-winged  than  diptera,  etc. 
A  few  scientific  terms,  such  as  mollusc  and  bivalve,  are 
in  such  common  use  that  they  may  be  readily  explained 
and  applied. 

Associated  facts  not  strictly  scientific — such  as  the 
uses  of  animals,  anecdotes  concerning  them,  their  pecu- 
liarities and  habits — which  the  pupils  themselves  may 
have  observed,  will  form  a  valuable  part  of  these  exercises, 
and  a  means  of  increasing  the  interest  of  the  lessons. 

The  pupils  should  be  encouraged  to  acquire  as  many 
facts  as  possible  by  their  own  observation  and  research 
out  of  school. 

The  exercises  should  be  conversational,  the  reviews 
frequent ;  the  instruction  should  also  embrace  exercises 
in  classifying  well-known  animals  from  a  miscellaneous 
list,  giving  the  reasons  in  each  case.  Too  much  ground 
should  not  be  attempted  at  first. 

Some  system  of  diagrams,  roughly  sketched  in  chalk, 
will  be  found  of  great  service  in  assisting  the  pupils  to 


132  HOW  TO  TEACH 

remember  the  classification.  The  best  and  simplest  is, 
probably,  that  used  in  the  ordinary  "genealogical  tree." 
The  diagram  should  be  gradually  developed  as  the 
lessons  proceed,  and  not  the  whole  of  it  given  in  the 
preliminary  stages. 

No  teacher  can  give  such  a  classified  "  outline  "  with- 
out having  first,  by  careful  study,  acquired  it.  This 
can  be  readily  accomplished  by  means  of  any  good  school 
manual  on  the  rudiments  of  Natural  History. 

Excepting  in  important  instances,  it  is  not  expected 
that  the  classification  should  extend  to  species  and 
variety,  sometimes  not  even  to  genera.  It  is  desirable 
that  the  pupils  should  have  some  definite  ideas  as  to  the 
relations  of  the  following  terms  used  in  zoology:  king- 
dom, branch  or  type,  class,  order,  family,  genus,  species, 
variety,  individual.  These  can  be  best  exhibited  by  a 
diagram,  but  they  should  in  no  case  be  presented  by 
formal  definition.  All  but  the  last  four  should  be 
mentioned  in  describing  any  given  animal. 

The  exercises  should  include  a  portion,  at  least,  of 
the  topics  suggested  in  the  following  synopsis,  which  is 
here  presented  for  the  guidance  of  the  teacher.  This 
synopsis  comprehends  three  successive  outlines,  each 
complete  in  it-self,  or  taken  with  that  preceding  it : 


FIRST  GENERAL,  OUTLINE. 

Distinction  of  organic  and  inorganic  objects  taught  objectively. 
Differences  between  animals  and  plants.  What  is  an  organ  f  An 
animal?  Four  great  types  of  animals  (Ciivier's,  and  omitting  the 
protozoa}.  Exercises  in  classifying,  by  types  only,  such  animals  as 
the  dog,  lobster,  clam,  coral,  shad,  wasp,  goose,  starfish,  yarter-snake, 
shrimp,  toad,  twtoise,  oyster,  etc.  The  reasons  for  the  classification 
should  be  given  in  each  case.  Each  type  to  be  then  briefly  de- 
fined. Why  vertebrates  are  placed  first. 


ELEMENTARY  SCIENCE.  133 

SECOND  GENERAL  OUTLINE. 

Classes  of  Vertebrates.  —  (Tenney's  arrangement  is  here 
selected  as  beiug  brief  and  simple,  but  any  other  may  be  taken.) 
Illustrate,  as  by  types,  by  mentioning  animals  belonging  to  the 
several  classes,  mammals  (those  which  feed  their  young  with 
milk),  birds,  reptiles,  batrachians  (frog  kind),  fishes  ;  brief  de- 
scription of  each  class  to  be  given.  Name  common  vertebrates 
to  be  classified,  occasionally  mentioning  an  animal  not  a  verte- 
brate, in  order  to  test  the  attention  and  accuracy  of  the  pupils  ; 
for  example  :  alligator,  robin,  mouse,  worm,  herring,  toad,  lion, 
,  rattlesnake,  elephant,  fan,  hawk,  turtle,  etc.,  etc. 


Classes  of  Articulates  to  be  treated  very  briefly,  but  in 
the  same  manner  us  the  vertebrates.  Simplest  division,  as  in- 
sects, crustacea,  and  worms,  to  be  employed. 

Classes  of  Molluscs.—  Trent  also  briefly,  by  referring  only 
to  their  general  characteristics.  Teach  the  meaning  of  the  terms 
univalve  and  bivalve.  Specimens  of  shells  will  be  useful  for  illus- 
tration ;  but  it  must  be  remembered  that  the  structure  of  the  ani- 
mal itself  is  far  more  interesting  and  important  than  that  of  the 
shell  which  incloses  it.  A  living  oyster  or  clam,  opened  and 
carefully  examined,  a  living  snail,  and  a  tumbler  of  water  con- 
taining a  few  of  the  small  molluscs  found  in  every  pond,  will 
give  clear  ideas.  A  small  aquarium  will  be  found  very  useful. 

Classes  of  Radiates,  probably  treated  with  sufficient  full- 
ness in  connection  with  types.  Review  if  necessary. 

Here  it  would  be  well  to  mention  the  grouping  of  animals  as 
Jierbivowus,  carnivorous,  and  omnivorov,s  ;  also  the  general  rela- 
tions of  the  teeth  of  animals  to  other  peculiarities,  such  as  feet, 
forms,  food,  disjestite  apparatus,  and  habits  ;  also,  as  far  as  may 
be  possible,  illustrations  of  the  importance  of  their  several  func- 
tions in  nature. 

THIRD  GENERAL  OUTLINE. 

In  this  outline  some  orders  should  be  omitted,  or  but  briefly 
considered,  because  not  readily  treated  objectively.  If  all  the 
prescribed  classes  cannot  readily  be  taught,  owing  to  the  limited 


134  HOW  TO  TEACH 

available  time,  selections  sufficiently  complete  in  themselves 
may  easily  be  made,  as  of  the  class  mammals,  or  birds,  or  of  the 
type  articulates. 


MAMMALS. 

Two-handed  (Bimana^—To  be  treated  briefly.  The  five  races 
of  men,  with  their  characteristic,  peculiarities.  The  geographi- 
cal distribution  of  each  to  be  also  briefly  referred  to. 

Four-handed  (Quadrumana.) — A  few  examples,  according  to 
the  experience  of  the  pupils.  Refer  to  the  geographical  distri- 
bution. 

Hand-winged  (Cheiroptera).— Use  a  drawing,  or  a  dried,  or  a 
living  specimen,  if  one  can  be  procured.  Any  interesting  facts 
about  bats,  and  their  nocturnal  habits. 

Insect-eaters  (Insectivora). — Treat  very  briefly.  The  mole,  its 
habits — refer  to  its  small,  hidden  eyes,  etc. 

Flesh-eaters  (Carniwra). — To  be  treated  more  fully.  Refer  to 
general  structure  of  teeth,  feet,  and  stomach.  Refer  to  cat  family, 
using  common  cat  as  type  ;  dog  family,  using  dog  as  type;  weasel 
family,  their  form,  habits,  etc.,  naming  sable,  marten,  ermine,  and 
mink,  and  referring  to  the  value  of  their  furs  ;  bear  family  ;  also 
briefly  to  seal  family. 

Pouched  Animals  (Marsupials'). — Refer  to  the  geographical  dis- 
tribution. The  exception  of  the  opossum. 

Gnawers  (Rodents).— Use  the  rat  or  squirrel  as  a  type.  Refer 
to  peculiarity  of  teeth,  and  the  provision  for  their  continued 
growth.  Teach  about  the  rat,  mouse,  squirrel,  beaver,  rabbit.  Re- 
fer to  the  woodcJiuck,  porcupine,  and  guinea-pig. 

Thick-skinned  (Pachyderms). — Treat  briefly  of  the  elephant,  the 
rhinoceros,  and  swine  families  ;  more  fully  of  the  horse  family,  in- 
cluding horse,  ass,  and  zebra.  Geographical  origin  of  the  horse, 
its  dispersion,  and  its  influence  in  human  affairs. 

Cud-chewers  (Ruminants). — Relations  of  food  to  teeth,  stomach, 
feet,  etc.,  etc.  Teach  three  families  :  1.  Deer  family,  horns  solid, 
deciduous ;  2.  Hollow-horned  family  (horns  permanent) ;  3.  Camel 
family  (hornless).  Refer  to  llama  and  vicuna. 

Whale-like  (Cetacea).— Refer  to  the  fish-like  character  of  tho 


ELEMENTARY  SCIENCE.  135 

whale  ;  how  it  differs  from  a  fish  ;  its  uses.    The  porpoise  and  the 
dolphin. 

NOTE.— Two  of  the  preceding  orders  (8th  and  9th),  are  sometimes  classified 
under  the  following  arrangement,  which  may  be  readily  substituted  for  the 
above  if  thought  desirable. 

Hoofed  (Ungulates)  into  two  sub-orders  :  A,  cud-chewers  (Euminants),  and 
Zf,  (Non-Ruminants).  These  are  again  divided  into  the  following  groups  of 
families:— 

A.  (Hollow-horned)  ox,  sheep,  and  antelope  families. 
(Solid-horned)  deer,  giraffe  families. 
(Hornless)  camel  family. 

E.  (Solid-hoofed)  horsu  family. 

(Thick-skinned  or  Pachyderms)  elephant,  swine,  hippopotamus,  rhinoceros, 
and  tapir  families. 

BlEDS. 

Birds  of  Prey  (Raptores). — Vulture,  falcon,  owl,  condor,  hawk, 
eagle. 

Ciimbers  (Scansores).— Parrot,  woodpecker,  etc. 

PercJwrs  (Insessores). — Humming  bird,  swallow,  kingbird, 
thrush,  sparrow,  canary,  etc. 

Scratchers  (Rasores). — Gallinaceous  birds  and  dove  family. 

Runners  (Cursores). — Ostrich  ;  its  habits. 

Waders  (Grallatores). — Crane,  stork,  snipe,  etc. 

Swimmers  (Natatores). — Duck  family  :  Swan,  petrel,  penguin, 
albatross,  etc.  Refer  to  nests  of  birds,  also  their  migrations,  in- 
stinct, etc. 

EEPTILES  AND  FROG  FAMILY. 

Treat  very  briefly,  teaching  something  of  turtles,  crocodiles, 
and  alligators;  serpents  and  their  fangs;  the  frog  and  its  trans- 
formations. 

FISHES. 

Treat  the  classification  very  briefly  ;  show  distinction  between 
the  two  groups,  bony  and  cartilaginous  fishes,  with  the  orders 
spine-finned  and  soft-finned  ;  also  the  shark  and  the  sturgeon. 

ARTICULATES. 

These  present  many  advantages  for  the  school-room.  They  are 
small,  and  easily  procured  for  perceptive  teaching.  A  simple 


136  HOW  TO  TEACH 

microscope  is  of  great  assistance  in  awakening  an  interest.  Of 
insects,  collections  of  type  specimens  can  easily  be  made.  Only 
the  simplest  and  most  interesting  facts,  however,  need  be  taught. 
The  general  characteristics  of  this  class  of  animals  should  be  ex- 
plained— their  structure  and  the  functions  of  their  chief  organs. 
Their  wonderful  transformations  should  be  explained  and  exem- 
plified ;  also  the  difference  between  insects  proper,  spielers,  and 
many-footed  articulates  (myriapods). 

The  following  orders  should  be  taught  and  exemplified : 

1.  Membrane-winged  (Hymenoptera). — Including  the  bee  family, 
the  ant  family,   the  icasp  family,  the  ichneumon  family,  their 
peculiarities,  habits,  and  instinct. 

2.  Scale-winged  (Lepidopterd). — Moths  and  butterflies,  how  dis- 
tinguished ;  caterpillars,  etc.,  clothes-moth,  geometer. 

3.  Tico-winged  (Diptera). — Mosquito  family,  wheat-fly,  house- 
fly, etc. 

4.  Case-winged  (Coleoptera}. — Beetle,  fire-fly,  weevil,  etc. 

5.  Half-winged  (Hemiptera) ;  or  bugs,  cicadas  or  harvest-flies, 
tree-hopper,  cochineal,  boat-fly,  etc. 

6.  Straight-winged (Orthoptera). — Cricket,  katydid,  locust,  grass- 
hopper. 

7.  Net-winged  (Neuroptera). — Dragon-fly,  May-fly.  Refer  to  the 
white  ants. 

Spiders  (Arachnida). 

Many-footed  Insect*  (Myriapods). — Centipedes. 

Crustacea. — Crab,  lobster. 

Worms. — Earth-worm. 

NOTE.— It  is  important  to  distinguish  carefully  the  three  terms,  insect  (i^e., 
six-footed  [hexapod].  or  true  insects),  arachnids,  or  eight-footed  spiders  nnd 
scorpions,  and  myrio/xxfa,  or  many-foe  ted  millipeds  and  centipedes.  In  using 
a  representative  of  one  of  these  groups  as  an  object,  it  should  be  the  primary 
aim  to  establish  the  obvious  characteristics  by  which  they  are  distinguished 
firmly  in  the  pupils'  minds.  Thus,  in  the  insect  proper,  the  body  is  divided 
into  three  divisions— the  head,  the  body  (or  thorax),  and  the  hind-body  (or 
abdomen).  The  head  is  furnished  with  feelers,  (antenna)  ;  the  body  supports 
three  pairs  of  legs,  and  generally  one  or  two  pairs  of  wings  ;  the  abdomen 
shows  more  or  less  clearly  a  number  (seven)  of  rings  or  joints.  In  the  arach- 
nids, the  head  and  body  are  consolidated  into  one  division,  which  has  no 
antenna;,  supports  four  pairs  of  legs,  but  no  wings.  In  the  myriapods,  the 
entire  body  consists  of  a  series  of  very  similar  joints,  not  grouped  into  divi- 
sions separated  (insected)  from  one  another,  but  of  which  the  first  serves  as  a 
head,  whilst  each  of  the  others,  however  numerous,  supports  i-ither  one  o» 
two  pairs  of  more  or  less  imperfect  legs. 


FOURTH    GRADE. 

OUTLINE   COURSE. 
Time  allowed,  about  five  months. 


LANGUAGE. 

Reading.—  Of  the  grade  of  a  Third  Reader  (latter  half),  with 
exercises  as  in  the  preceding  grade. 

Spelling  and  Definitions.—  From  the  reading  lessons, 
with  exercises  in  miscellaneous  words  and  sentences,  as  in  the 
preceding  grade.  Also  easy  exercises  on  the  prefixes  and 
suffixes,  and  their  applications. 

English  Grammar.  —  To  include  the  analysis,  parsing,  and 
construction  of  simple  sentences,  and  with  such  definitions  only 
as  pertain  to  the  parts  of  the  subject  studied. 

ARITHMETIC. 

Mental  Arithmetic.  —  As  far  as  in  written  arithmetic,  with 
exercises  as  in  the  Fifth  Grade,  including  practice  in  the  simple 
applications  of  the  tables  of  weight,  measure,  money,  etc. 

Written  Arithmetic.  —  Common  and  Decimal  Fractions, 
with  their  simple  practical  applications,  and  their  conversion  one 
into  the  other.  Also,  practice  in  the  simple  rules  and  Federal 
Money,  for  the  purpose  of  securing  rapidity  and  accuracy. 


GEOGRAPHY. 

Geography.—  Of  the  United  States  in  detail.    Local  and 
descriptive  geography  treated  as  in  the  Fifth  Grade. 


138  HOW  TO  TEACH 


ELEMENTARY   SCIENCE     FOR    ORAL    INSTRUCTION. 

Botany. — An  outline  knowledge  of  Botany,  including  the 
general  structure  and  common  uses  of  such  plants  as  mort 
pupils  may  readily  observe. 

This  should,  if  possible,  be  taught  during  the  spring  and 
summer  months,  in  order  to  make  it  in  the  highest  degree  ob- 
jective by  the  use-  of  specimens. 

Mineralogy. — A  simple  outline  knowledge  of  Mineralogy, 
illustrated  by  specimens. 

This  may  constitute  the  fall  and  winter  course,  the  specimens 
being  previously  collected.  When  the  time  permits  the  teaching 
of  only  one  of  these  branches,  the  season  of  the  year  should 
determine  the  choice  between  them. 


WRITING. 

On  Slates. — Continued  with  practice,  to  give  expertness  and 
fluency. 

On,  Paper. — Review  of  the  elementary  forms  ;  their  com- 
bination in  words  containing  long  and  short  letters,  without 
capitals  ;  next,  in  words  containing  both  capitals  and  small 
letters  ;  an  explanation  of  the  elements  involved  in  each. 

Instruction  as  to  proper  position,  holding  the  pen,  etc.,  as  in 
the  preceding  grade. 

DRAWING. 

On  Slate  or  Pitpf-r. — Review  of  the  Fifth  Grade  as  far  as 
may  be  necessary,  ajid  drawing  curve  lines,  and  figures  formed 
frqm  them,  as  the.  circle,  ellipse,  etc.  ;  also  simple  designs  con- 
taining straight  and  curved  lines. 


SPELLING. 


How  TO  TEACH 


SUBJECTS     OF     THE     FOURTH     GRADE. 


LANGUAGE. 

Heading. — See  directions  and  suggestions  given 
for  the  Fifth  Grade. 

The  latter  half  of  a  Third  Eeader  usually  comprises 
selections  appropriate  to  this  grade.  Particular  atten- 
tion should  be  given  to  clearness  of  articulation,  to 
naturalness  of  intonation,  and  to  general  style. 

Spelling. — The  exercises  in  spelling,  both  oral  and 
written,  should  be  the  same  as  in  the  previous  grade, 
with  the  following  additional  suggestions.  The  names 
of  important  cities,  states,  and  countries,  which  occur 
in  the  geographical  lessons  of  the  class,  and  especially 
such  as  are  in  frequent  use  in  post-office  addresses,  or 
are  liable  to  be  mis-spelled,  should  form  a  part  of  the 
miscellaneous  words  taught  in  this  grade ;  also,  familiar 
personal  names.  An  excellent  occasional  modification 
of  this  exercise  is,  to  have  the  pupils  draw  the  out- 
line of  a  letter-envelope  upon  the  slate,  or  use  a  neatly- 
trimmed  piece  of  writing  paper  of  the  same  shape,  and 
direct  it  to  some  person  whose  address  is  given  by  the 
teacher.  The  ingenuity  of  the  teacher  will  suggest 
many  other  similar  modifications  of  the  exercise. 


140  HOW  TO  TEA  OH 

Definitions.  —  These  should  be  as  in  the  previous 
grade,  with  the  following  additional  exercises  designed 
to  lead  to  the  study  of  etymology. 

"  The  easy  exercises  on  the  prefixes  and  suffixes  " 
should  be  Avith  English  primitives  at  first,  without  re- 
gard to  the  etymology  of  those  primitives.  The  affixes 
of  Anglo-Saxon  origin  will  therefore  be  taught  first; 
afterward  the  meaning  of  such  as  ab,  con,  pre,  pro,  sub, 
ion,  ent,  etc.,  may  be  taught  as  illustrative  of  the  diver- 
sity of  meaning  of  such  words  as  abstract,  subtract,  con- 
cede, accede,  precede,  etc.  Also  as  showing  that,  for 
example,  all  words  having  the  prefix  sub  convey  the 
signification  of  under,  and  all  having  the  suffix  ion 
mean  the  act  of. 

2.  Each  group,  with  its  common  radical  or  primitive, 
after  being  written  on  the  slate  or  blackboard,  should  be 
made  the  subject  of  an  oral  exercise  in  definitions,  in 
order  to  impress  upon  the  pupils'  minds  the  modifica- 
tions of  meaning  produced  by  the  affixes.  The  exem- 
plification of  the  words  in  sentences  should  be  also  care- 
fully attended  to. 


Grammar.  —  The  instruction  in  this 
subject  required  for  the  Fourth  Grade  includes  analysis, 
parsing,  and  construction,  and  in  the  order  mentioned. 
Grammar  is  the  science  of  the  sentence  ;  and,  therefore, 
the  fundamental  idea  to  be  imparted  is,  what  consti- 
tutes a  sentence.  Oral  lessons  should  precede  the  study 
of  the  text-book,  as  a  preparation  for  it.  The  ideas  in- 
volved in  the  definitions  should  first  be  developed,  before 
the  pupils  are  required  to  commit  these  definitions  to 
memory.  The  contrary  practice,  once  so  common,  is 


LANGUAGE.  141 

very  discouraging  and  injurious  to  the  pupil,  since  it 
compels  him  to  learn  by  rote  a  mass  of  verbiage  which 
is  perfectly  unintelligible  to  him. 

Let  a  short  sentence  be  written  on  the  slate  or  black- 
board ;  and  then,  by  analysis,  let  the  pupils  be  made 
familiar  with  the  relations  of  the  words  used  as  subject, 
verb  or  predicate,  and  adjuncts,  or  modifiers.  The  dis- 
tinctions comprehended  in  the  parts  of  speech  can  all 
be  successively  taught  in  this  way,  and  the  pupil  en- 
abled readily  to  point  them  out,  before  he  is  required  to 
say  what  a  noun,  or  pronoun,  or  verb,  etc.,  is.  The 
learning  of  the  definitions  will  be  easily  accomplished  as 
he  proceeds. 

The  object  of  the  analysis  is  to  find  out  in  what  rela- 
tion the  words  used  in  the  sentence  stand  to  one  another 
(general  grammar) ;  the  object  of  the  parsing  (only  an- 
other kind  of  analysis)  is  to  apply  the  principles  and 
rules  proper  to  these  relations  (particular  grammar) ;  the 
object  of  the  construction  is  to  impart  practical  skill  in 
applying  these  rules  and  principles,  as  well  as  to  give 
thereby  clearer  ideas  of  their  nature  and  use.  Thus, 
when  the  teacher  presents  the  sentence,  "  Industrious 
pupils  learn  very  rapidly,"  the  pupil  is  made  to  discover, 
first,  the  principal  parts — subject  and  verb,  or  simple 
predicate  ;  next,  that  industrious  is  added  to  pupils, 
rapidly  to  learn,  and  very  to  rapidly.  The  pupil  then 
knows  that  industrious,  being  an  adjunct  of  a  noun,  is 
an  adjective ;  that  rapidly,  being  an  adjunct  of  a  verb,  is 
an  adverb ;  and  that  very,  being  an  adjunct  of  an  adverb, 
is  also  an  adverb.  This  instruction  can  be  supplemented 
by  requiring  the  pupils  to  construct  sentences  of  a 
similar  kind  ;  as,  sentences  containing  a  simple  subject 
and  predicate, — sentences  containing  a  subject  and  ad- 
juncts with  a  simple  predicate, — sentences  containing  a 


142  HOW  TO  TEACH 

subject  and  predicate,  with  adjuncts  of  both.  Some  of 
these  sentences  may  be  required  to  be  declarative,  some 
interrogative,  etc.  In  this  way  the  ingenuity  or  inven- 
tion of  the  pupil  is  brought  into  play  in  connection  with 
his  knowledge  of  grammar  ;  and  the  exercises  glide  pro- 
gressively into  extended  composition. 

The  sentences  presented  should  at  first  be  carefully 
classified,  so  that  no  difficulties  maybe  presented  which 
are  beyond  the  pupils'  ability  or  actual  attainments  to 
solve.  In  grammar,  especially,  should  the  instruction 
be  systematic  and  logical. 

Etymological  exercises  should  be  interspersed,  espe- 
cially in  the  use  of  the  apostrophe  as  the  sign  of  the 
possessive  case — in  the  proper  plural  termination  of 
nouns — the  proper  forms  of  the  pronouns,  etc.  This  is 
a  point  of  considerable  importance. 

The  sentences  required  to  be  studied  in  this  grade  in- 
clude : 

1.  Sentences  with  a  simple  subject  and  a  simple  pred- 
icate; 2.  Those  with  simple  word  adjuncts  of  either  sub- 
ject or  predicate,  or  both  ;  3.  Those  with  simple  phrase 
adjuncts  (so  as  to  teach  the  preposition] ;  4.  Those 
with  compound  subjects  or  compound  predicates,  or 
both,  but  of  an  easy  character  ;  as,  "  John,  William,  and 
Samuel  are  diligent  boys," — "The animals  turned,  look- 
ed, and  ran  away."  This  class  of  sentences  will  serve 
to  introduce  the  conjunction. 

It  is  especially  requisite  in  all  the  lessons  given  on 
this  subject,  that  the  instruction  should  not  be  allowed 
to  degenerate  into  the  repetition  of  formulae,  and  instead 
of  being  made  a  means  of  developing  the  analytic  and 
reasoning  faculties  of  the  pupils,  become  a  piece  of 
worse  than  useless  mechanism.  Grammatical  instruc- 


LANGUAGE.  143 

tion  has  a  distinct  office  as  an  educational  agent, — an 
office  that  can  be  performed  by  no  other  subject.  It  is 
addressed  to  faculties  that  probably  cannot  be  trained 
in  any  other  way ;  and,  therefore,  no  educational  cur- 
riculum would  be  complete  without  it.  It  should,  how- 
ever, be  carefully  kept  within  proper  limits,  both  as  to 
time  and  place,  and  should  not  be  permitted  to  encroach 
upon  other  branches  of  equal  importance.  Each  depart- 
ment of  it  should  also  have  its  due  share  of  attention. 

Of  course  the  study  of  grammar  as  prescribed  in  this 
grade  does  not  supersede  the  "  exercises  for  correction  " 
required  in  all  the  grades.  These  exercises,  however, 
by  degrees  lose  their  empirical  character,  and  become 
scientific.  They  should  not  be  exclusively  either  ety- 
mological or  syntactical,  according  to  the  technical  dis- 
crimination followed  in  most  text-books  on  English 
Grammar.  Indeed,  nothing  has  done  more  to  bring 
upon  this  study  an  unmerited  depreciation,  as  being  a 
senseless  waste  of  time,  than  the  unwise  separation  of 
these  correlated  departments  of  the  subject. 

For  instance,  instead  of  teaching  the  declension  of 
the  pronouns  /,  thou,  he,  and  she,  long  before  the  appli- 
cation of  any  syntactical  rule,  the  diversities  of  inflec- 
tion and  their  proper  use  may  be  observed  and  studied 
by  the  pupil  in  connection  with  the  ordinary  analysis 
of  simple  sentences,  and  consequently  at  a  quite  ele- 
mentary stage  of  the  study.  The  transformation  of 
"John  can  see  James"  into  "/can  see  him,"  will  teach 
him  the  nature  of  a  pronoun,  how  to  distinguish  it,  and 
then  how  to  define  it.  An  attempted  change  of  places, 
as  in  "  Him  can  see  I,"  when  taken  in  connection  with 
the  analysis,  will  show  him  the  reason  of  the  change  of 
form  from  he  to  him  and  from  /  to  me. 

Similar  exercises  upon  the  other  pronouns,  used  in 


144  SOW  TO  TEACH 

both  numbers,  will  lead  him  to  see  that  each  of  them 
takes  one  form  when  used  as  the  subject  of  a  sentence, 
and  a  different  one  when  used  as  the  object.  He  will 
then  be  ready  to  use  intelligently  the  terms  singular, 
plural,  nominative,  and  objective,  as  applied  to  varied 
inflections,  and  to  correct  Birch  errors  as,  "  Who  saw 
him  ?  Me."  "  Me  and  her  saw  him,"  etc.,  as  well  as  to 
give  the  reason  for  such  corrections.  Then,  and  not 
till  then,  can  he  bs  profitably  required  to  construct,  re- 
peat, and  explain  the  declensions  of  the  pronouns.  A 
similar  plan  should  be  followed  in  the  comparison  of 
adjectives  and  the  conjugation  of  verbs. 

A  few  common  errors  are  subjoined  as  a  further  illus- 
tration of  the  kind  of  work  proper  to  this  grade. 

ERRORS  IN  ETYMOLOGY. — 1.  The  Possessive  Sign.  A  goos'es 
foot.  Three  gecses'  heads.  Two  fox's  tails.  A  mans  hat. 

2.  Improper  form  of  tenses.  They  done  it.  We  seen  him. 
He  would  have  went.  If  I  had  have  seen  it. 

8.  Improper  use  of  verbs.  He  must  set  still.  The  book  lays 
on  the  desk.  H^  1'iid  still. 

ERRORS  IN  SYNTAX  — 1.  Subject.  Me  and  her  can  sew 
2.  Predicate.  We  was  there.  He  don't  know.  She  dare  not 
do  it.  3.  Object.  He  struck  my  brother  and  I.  Who  did  you 
see  ?  Attribute.  If  I  were  him.  She  looks  beautifully. 


ARITHMETIC. 

Mental  Arithmetic* — The  character  of  the  ex- 
amples to  be  given  in  this  grade  is  suggested  by  the 
exercises  in  AVritten  Arithmetic.  The  same  processes 
and  forms  of  analysis  should  be  employed  in  both.  In 
connection  with  the  commonly-used  tables  of  weight, 
measure,  etc,  should  be  given  such  questions  as,  "In 
|  of  a  pound  of  sugar,  how  many  ounces?"  "18 
quarts  are  what  part  of  a  bushel  ?  "  etc.,  etc. 


ARITHMETIC.  145 

Written  Arithmetic. — Federal  Money  should 
also  form  a  part  of  the  regular  work  of  this  grade  at 
least  once  a  week,  and  should  be  frequently  reviewed. 

Particular  care  should  be  taken  in  the  selection  of 
examples  that  no  one  of  them  be  so  intricate  and  prolix 
as  to  consume  a  large  amount  of  time,  without  afford- 
ing sufficient  exercise  of  thought  in  the  application  of 
arithmetical  principles. 

Too  much  importance,  nevertheless,  can  scarcely  be 
given  to  the  requirement  of  "practice  for  rapidity  and 
accuracy"  in  Federal  money,  as  well  as  the  simple  rules 
of  Arithmetic.  To  this  should  invariably  be  assigned  a 
brief  portion,  at  least,  of  the  time  given  to  every  lesson 
in  this  subject.  No  part  of  the  arithmetical  discipline 
has  a  higher  utilitarian  value,  whether  for  the  purposes 
of  practical  life,  or  for  progress  in  the  more  advanced 
portions  of  the  study ;  for  nothing  is  more  discouraging 
to  the  pupil  than  to  find  that,  in  any  exercise  involving 
other  than  a  few  figures,  his  results  are  almost  always 
incorrect,  from  a  want  of  habitual  accuracy  in  perform- 
ing the  simple  combinations  involved  in  the  elementary 
rules.  Teachers  are,  therefore,  especially  advised  to 
employ  every  variety  of  proper  stimulus  to  make  the 
exercises  for  this  purpose  thorough  and  effective. 

For  general  suggestions  see  the  preceding  grade. 

Common,  Fractions. — No  part  of  the  study  of 
arithmetic  is  of  more  importance  than  the  subject  of 
fractions.  When  properly  taught,  their  value,  as  a 
mental  discipline,  is  of  the  highest  order.  When 
taught  merely,  or  chiefly,  by  memorized  formula?, 
called  "  rules,"  they  are,  for  the  greater  part,  a  wasto 
of  precious  time. 

No  principle  should  be  presenter  until  the  pupil  u 


[4:0  HOW  TO  TEACH 

about  to  make  use  of  it,  and  no  definition  should  be  given 
or  required  before  the  ideas  which  it  embodies  have  been 
deduced,  and  clearly  presented  by  preliminary  illustra- 
tion and  questioning. 

No  rules  should  be  given  until  a  sufficient  number 
of  examples  for  practice  have  made  them  a  succinct 
statement  of  principles  previously  understood,  or  the 
results  of  the  application  of  principles,  rather  than  mere 
mechanical  formulae  for  working. 

In  teaching  the  fundamental  principles  of  fractions 
the  objective  process  is  indispensable. 

The  most  effective  method  of  treating  the  subject  as 
a  whole,  is  to  give  first  a  very  simple  outline  course  of 
exercises,  covering  all  the  essential  principles,  but  by 
means  of  examples  requiring  only  small  numbers  for 
their  solution.  Such  examples,  though  readily  solved 
mentally,  after  some  practice,  should,  in  the  first  stages, 
be  wrought  upon  the  slates,  in  order  to  secure  correct- 
ness in  notation,  and  to  allow  the  pupil  more  easily  to 
give  the  necessary  analysis  without  the  additional  men- 
tal tax  required  by  the  effort  to  retain  the  numbers. 

In  the  written  exercises  pupils  should  use  the  signs 
of  operation,  +  —  x  -h,  and  the  sign  of  equality,  to 
indicate  the  work  performed,  and  its  result. 

This  outline  should  then  be  followed  by  a,  full  course, 
in  which  the  substance  of  the  first  constitutes  the  exer- 
cises in  mental  arithmetic,  while  the  written  arithmetic 
comprises  the  more  difficult  portions  of  the  general  sub- 
ject, as  well  as  a  systematic  statement  of  definitions 
and  rules,  and  practical  examples,  involving  numbers 
too  large  to  be  readily  retained  in  the  memory.  Such  a 
plan,  though  apparently  long,  is  in  reality  the  most  ex- 
peditious. The  pupil  soon  obtains  a  clear,  comprehen- 
sive, and  connected  view  of  the  essential  principles,  and 


ARITHMETIC.  147 

the    expanded   review   which    constitutes    the   second 
course  will  then  require  but  little  time. 


SYLLABUS  OF  TOPICS  FOR  OUTLINES  OF  COMMON 
FRACTIONS. 

(WITH   SUGGESTIONS   AND   EXAMPLES.) 

I. — The  idea  of  a  fractioii  developed  objectively. 

The  equality  of  the  parts  to  be  very  carefully  illustrated. 

The  relative  value  of  various  fractional  parts,  as  greater  or  less, 
as  i,  i,  -/u,  etc. 

The  definition  of  a  fraction.  One  or  more  of  the  equal  parts 
of  a  unit 

The  terms  of  a  fraction  defined  and  the  order  of  statement. 

The  notation  of  fractions  and  location  of  terms,  or  order  of 
writing. 

Exercises  in  writing  and  explaining  fractions. 

Fractional  expressions  less  than  a  unit. 

Proper  fractions  denned,  and  examples.  A  proper  fraction  is 
one  that  is  less  than  a  unit. 

Fractional  expressions  equal  to  or  greater  than  a  unit. 

Improper  fractions  defined  and  illustrated.  An  improper  frac- 
'.ion  is  one  that  is  equal  to,  or  greater  than  a  unit. 

Exercises  in  writing  proper  and  improper  fractions. 


n 
II. — FUNDAMENTAL,  AXIOM  1=  - 

n 

Reduction  of  units  to  improper  fractions.  —  Analysis  A. 
(Page  152.) 

Reduction  of  mixed  numbers  to  improper  fractions. — Analysis  A. 

Definition  of  mixed  numbers. 

Exercises  in  mixed  numbers,  limited  to  small  denominators. 

Reduction  of  improper  fractions  to  mixed  numbers. — Analysis  B. 
(Page  152.) 


148  HOW  TO  TEACH 

III. —  Reduction  of  fractions  to  greater  denominators — or  higher 
terms.  [What  may  halves,  thirds,  etc.,  be  changed  into  ?  f's?etc.J 
To  be  illustrated  objectively.  . 

Examples  with  greater  denominators  than  can  readily  be  solved 
by  inspection. 

Analysis  C.    (Page  152).     (Begin  with  fundamental  axiom.) 

Term  Divisor  or  Factor,  with  exercises  in  finding,  by  inspection 
only,  a  Common  Divisor  or  Common  Factor.  Definition  to  be 
given. 

NOTE.— Too  great  importance  can  hardly  be  given  to  this  exercise  of  in- 
spection. The  application  of  the  principle  is  indispensable  in  many  of  the 
arithmetical  exercises  in  every  succeeding  grade.  With  proper  training,  it 
will  become,  within  reasonable  limits",  a  fixed  mental  habit,  requiring  no  con- 
scious effort. 

Reduction  of  Fractions  to  Lower  Terms  or  Less  Denominators — 
Examples — Analysis  D.  (Page  152).  Definition  of  "Lowest 
Terms." 

Examples 'n  finding  what  part  one  whole  number  is  of  another 
^-corresponding  examples  in  tables. 

IV. — Multiple — term  illustrated  and  defined. 
Common  Multiple  " 

Exercises,  to  be  solved  by  inspection. 

Reduction  to  Common  Denominator — use  two  fractions  only. 

Application  of  common  multiple  in  reducing  to  common 
denominator. 

Distinction  between  common  multiple  and  common  denomi- 
nator. 

Definition  of  common  denominator. 

"  least  common  denominator. 

Examples  in  reducing  to  least  common  denominators. — 
Analysis  C. 

Examples  involving  previous  reduction  to  lowest  terms,  by  in- 
spection. Reduce  f  J  and  ,&5  to  their  least  common  denomi- 
nator. 

Use  of  common  denominator  as  the  simple  but  indispensable 
basis  for  the  working  and  explanation  of  Addition,  Subtraction, 
and  Division  of  Fractions. 


ARITHMETIC.  149 

V. — Impossibility  of  adding  quantities  with  unlike  names, 
illustrated  :  Add  3  elms  and  4  oaks ;  add  3  trees  and  4  trees  =  7 
trees. 

In  teaching  tlie  elementary  principles,  the  subject  of  fractions 
should,  as  far  as  possible,  be  divested  of  technicalities,  and  be 
made  to  coincide  with  the  acquired  experience  and  simple 
notions  of  a  child. 

On  this  account  it  is  much  better  at  first,  to  say,  find  %  of  f, 
than  to  say,  multiply  f  by  §,  or  find  f  times  §. 

Adding  things  of  like  names. 

Adding  fractions  of  the  same  denominator — Examples. 

Adding  fractions  of  different  denominators — Examples  — 
Analysis  C.  (Page  152). 

Necessity  of  reducing  to  common  denominator. 

The  numerators  only  added ;  why  ? 

NOTE.— In  no  example  give  more  than  two  fractions.  The  common 
denominator  to  contain  not  more  than  two  digits. 

Addition  of  small  mixed  numbers — Examples — Analysis  C. 

NOTE.— See  that  the  sign  of  operation  and  the  equality  sign  are  not  omitted. 
Avoid  reducing  to  improper  fractions. 

Rule. — 1st.  See  that  the  fractions  are  in  their  lowest  terms  ;  2d. 
Reduce  to  common  denominator  ;  3d.  Add  their  numerators,  etc. 

Subtracting  fractions  of  different  denominators — Analysis  C. 

Rule. — 1st.  See  that  the  fractions  are  in  their  lowest  terms  ;  2d. 
Reduce  to  common  denominator ;  3d.  Subtract  the  less  nume- 
rator from  the  greater,  etc. 

The  same  examples  may  be  used  as  in  addition. 

Questions  should  be  occasionally  varied  by  asking:  "Which  is 
the  greater  ?  "  or  "  What  is  the  difference  ?  " 

1 1st.  Reducing  to  improper  fractions. 

NOTE.— In  mixed  numbers  avoid -j  3^    The  difficult  case,  7i— 2«  (deferred 

to  review.) 

VI.—"  Multiplication  of  fractions  "  and  "  compound  fractions  " 
identical. 

Such  expressions  as  £  of  2|,  f  of  \,  etc.,  only  involve  the  find- 
ing of  a  fractional  part,  and  should  be  treated  at  first  as  such, 
rather  than  as  a  special  kind  of  fractions. 

It  must  not  be  forgotten  by  the  teacher  that  from  the  nature  and 
definition  of  a  fraction,  every  example  in  fractions  must  involve 
or  relate  to  division  in  some  way. 


150  IIOW  TO  TEACH 

There  are  two  cases  in  the  so-called  multiplication  of 
fractions : 

1st.  Where  a  fraction  or  mixed  number  is  to  be 
actually  multiplied.  In  this  case  the  multiplier  must 
be  a  whole  number — as  3  times  -|,  or  3  times  4f. 

2d.  Where  a,  fractional  part  is  to  be  taken  of  either  a 
whole  number,  or  of  a  fraction,  or  of  both;  as  •§  of  17, 
or  |  of  4 ,  or  |  of  7f 

NOTE.— Mntliplication  by  a  mixed  number  is  a  combination  of  the  1st  and 
2d  cases. 

Only  in  the  first  case  should  the  expression  "#wes"  be  wed. 

In  the  second  case  the  expression  "qf"  only  should  be  used. 

In  the  case  of  multiplying  by  a  mixed  number,  the  expression  "  limes'1''  is 
used  for  conciseness,  though  not  logically  correct.  The  proper  expression  is 
too  cumbersomein  practice — "  4  limes  the  number  and  %  of  the  number." 

Only  the  two  varieties  of  the  first  case,  and  the  first  two  varieties  of  the 
second  case  should  be  required  until  the  subject  is  reviewed. 

Examples  :  fl  times  t Analysis  as  in  simple 


I       x  ,  then  B.     (Page  152). 


Multiplication  OF  Fractions  1  7  times    4| Analysis    as    in 

l^     simple  x  ,  then  B.     (Page  152). 

f  i  of  24;  4|  of  $24.    No  analysis, 

{except  reducing  to  lowest  terms. 
|  of  25 ;  M  of  $25.  Analysis  E. 
(Page  152). 

I  |  of  f- ;  }f  of  £.  Analysis  F.  (Page 
[     152). 

For  rule  and  its  origin,  see  Analysis  F. 

Examples  to  be  given  in  the  practical  form  at  as  early  a  stage 
as  can  be  made  expedient. 

Find  how  many  cents,  or  cents  and  mills,  in  a  given  fraction 
of  a  dollar. 

Occasional  examples  involving  preliminary  reduction  to  lowest 
terms. 

Rule. — 1st.  See  that  the  fractions  are  in  their  lowest  terms  ;  2d. 
Multiply  the  numerators  for  new  numerator,  and  the  denomina- 
ters  for  a  new  denominator. 

Solutions  by  direct  cancellation  should  not  be  required  until  the 
review. 


ARITHMETIC.  151 

VII.  There  are,  theoretically,  two  cases  in  the  Divis- 
ion of  Fractions : 

1st.  Division  OF  a  FRACTIONAL  NUMBER  by  an  inte- 
gral number,  as  f  -f-  7,  and  4|  -4-  7 ;  evidently  identical 
with  \  of  f ,  and  \  of  4|  in  the  so-called  multiplication 
of  fractions. 

3d.  Division  of  any  number,  integral  or  fractional,  BY 

A  FRACTIONAL  NUMBER,  OB  5  •*-  f  ,  f  -*-  f  ,  8f  -r  f ,  8-|  -f-  9$. 

The  form  of  putting  the  questions  should  be  varied  as  much 
as  possible,  so  as  to  train  pupils  to  select  and  apply  the  right 
principle  and  method.  Sometimes  the  divisor,  sometimes  the 
dividend,  should  be  first  named. 

"  How  many  times  are  4|  contained  in  9  ?  "  Use  this  form  of 
questioning  at  least  as  frequently  as  the  more  technical  form, 
Divide  9  by  4£. 

The  two  varieties  of  the  first  case,  and  the  first  two  varieties 
only  of  the  second  case,  should  be  required  before  the  review. 

Samples  in  Division  of  and  by  Fractions — Analysis  : 

The  method  and  analysis  to  be  by  common  divisor.  The  first 
case  may  also  be  analyzed  by  Analysis  F  (page  152),  if  desired. 

The  method  by  inverting  the  divisor  is  deferred  to  the 
review.  See  Note  1  under  Analysis  G  (page  153.) 

Rule. — 1st.  See  that  the  fractions  are  in  their  lowest  terms ; 
3d.  Reduce  to  a  common  denominator  ;  3d.  Divide  the  numerator 
of  the  dividend  by  the  numerator  of  the  divisor. 

Examples  in  finding  what  p;vrt  one  fractional  number  is  of 
another.  Begin  with  integers  :  5  are  what  part  of  8  ?  8  what 
part  of  11  ?  (Analyze  from  the  unit,  1  is  £  of  8,  5  are  $  of  8, etc., 
etc.) 

|  are  what  part  of  \  ?  f  are  what  part  of  J  ?  etc.,  etc. 


152  SOW  TO  TEACH 

Practical  Examples:  (  If  7  yards  cost  $J,  what  will  a  yard  cost?) 
1st  Group.         \  "  8  yards    "     $4|,    "       "          "        "     f 
f  If  a  yard  cost   $£,  how  much  can  be") 
3d  Group          J      bought  for  $8  ? 

j  If  a  yard   cost  $£,  how  much  can  be 
[     bought  for  $|  ? 

0,1  pwi.  j  If  I  yard  cost  $5,  what  will  a  yard  cost?  ) 

ou  wnmp.  1   «  a     «       "      *5.      «         c  ««         u       r 

$>b>  ) 

FORMS  OF  ANALYSIS  FOR  THE  OUTLINES  OF   COMMON  FRACTIONS. 

Analysis  A. — Example. — Reduce  5^  to  halves,  or  to  an  improper 
fraction  :— 1  =  f ;  5  =  5  times  \—^\  ^  +  i  =  V-- 

Analysis  B. — Example. — Reduce  ^  to  units,  or  to  a  mixed 
number  : — 1  =  f ;  hence,  in  ^  there  are  as  many  units  as  f  are 
contained  times  in  -£-,  equal  to  7^. 

Analysis  C. — Example. — Reduce  §  to  ninths : — In  a  unit  there 
are  f ;  hence  ^  =  f,  and  §  =  2  x  f  =  § . 

NOTE.— Avoid  saying  "a  whole  number,"  or  "  one  whole  number,"  when 
speaking  of  a  unit. 

Analysis  D. — Example. — Reduce  ||  to  its  lowest  terms  : — By 
inspection  the  greatest  common  divisor  is  6,  hence  it  may  be  re- 
duced to  thirds  ;  -,a8-  =  £ ;  hence  there  are  as  many  thirds  as  -fa  are 
contained  times  in  f  f ,  or  taw-thirds — f. 

Analysis  E. — Example. — Find  |  of  25.  ^  of  25  is  8^ ;  |  of  25  are 
3  times  3£  =  9| ;  or  (using  as  a  basis  the  Axiom  f  of  a  unit  =  ^  of 
3  units  ;  f  =  \  of  3,  first  illustrating  objectively  by  lines  divided 
into  parts),  f  of  25  =  i  of  3  times  25  =  i  of  75  =  9|.  The  former 
process  is,  in  many  respects,  preferable. 

Analysis  F. — Example. — Find  f  of  f .  (First,  as  a  basis,  show 
OBJECTIVELY  that  i  of  i  =  i ;  i  of  £  =  £ ;  £  of  \  =  -,1.,- ,  etc.,  etc.) 
i  of  |  =  j&  ;  i  of  f  =  5  times  -A  =  -&  ;  $  of  $•  =  3  times  -&  =  M- 

NOTE  1st.— Make  the  same  question  "  practical,"  and  apply  the  earn* 
analysis.  If  a  yard  cost  $7,  how  much  will  f  of  a  yard  cost?  It  will  cost$ 
of  f  of  a  dollar,  etc.,  etc.,  as  before- 

NOTE  2d.—  After  a  few  simple  examples  have  been  carefully  analyzed, 
point  out  the  numerical  relation  of  the  numerator  and  the  denominator  of  the 
product  to  those  of  the  factor?,  and  then,  not  before,  deduce  or  give  the  follow- 
ing 

Rule-  for  the  Multiplication  of  Fractions : 

1st.  See  that  the  fractions  are  in  their  lowest  terms ;  2d.  Mul- 


ARITHMETIC.  153 

tiply  the  numerators  for  the  numerator  of  the  product;  and 
multiply  the  denominators  for  the  denominator  of  the  product. 

Analysis  G. — Example. — If  a  yard  costs  $£,  how  much  can  be 
bought  for  $£  ? 

(See  Analysis  B,  5th  Grade,  to  be  combined  with  reduction  to 
Common  Denominator.) 

If  a  yard  cost  $|,  $$  will  buy  as  many  yards  as  $$  are  con- 
tained times  in  $$,  or,  reducing  to  Common  Denominator,  f  = 
f  *>  i  =  £i>  as  many  yards  as  H  are  contained  times  in  $f ,  or  2-/r 
yards. 

NOTE  1st.— To  "invert  the  divisor  and  proceed  as  in  multiplication,"  is 
much  more  concise  as  a  method,  but  it  is  not  in  any  sense  an  analysis,  but  a 
condensed  and  valuable  rule,  which  is  to  be  both  taught  and  analyzed  in  the 
review.  When  this  concise  rule  is  taught  before  the  analysis  by  reducing  to 
a  common  denominator,  the  teacher  will  usually  find  three  undesirable  results: 
first,  the  pupils  are  as  likely  to  invert  the  wrong  fraction  as  the  right  one, 
unless  the  question  is  a)  way?  put  in  one  particular  way,  and  even  then,  until 
after  much  practice  ;  thus  showing  that  they  arc  not  guided  by  any  principle  : 
second,  they  cannot  explain  the  process  ;  and  third,  it  is  then  much  more 
difficult  to  teach  the  analysis,  because  their  minds  are  preoccupied  by  the 
brief  rule,  which  naturally  seems  to  them  so  much  more  desirable,  as  it  costs 
little  or  no  mental  effort. 

As  the  study  of  fractions  is  an  important  i»iental  discipline,  any  course 
which  practically  excludes  the  fundamental  principle  of  division  by  a  fraction 
should  be  careiully  avoided. 

NOTE  2d.— It  will  be  perceived  that  the  analysis  of  the  division  of  ono  frac- 
tion by  another  by  the  process  of  reducing  to  a  common  denominator,  is  essen- 
tially identical  with  the  analysis  of  reducing  an  improper  fraction  to  a  whole 
or  mixed  number. 

Analysis  H.— Example.— If  f  of  a  yard  cost  $|,  what  will  a 
yard  cost  ? 

(See  Analysis  C,  in  5th  Grade,  with  which  the  following  is  es- 
sentially identical.) 

If  }  of  a  yard  cost  $  J,  I  of  a  yard  will  cost  i  of  $|  (note  that  this 
division  by  the  numerator  is  the  vital  step  in  the  process),  which 
is  $-&  ;  and  a  yard  or  \  will  cost  7  times  $-&,  or  $|i,  equal  to  $lvV 

NOTE  1st.— This  is  one  of  the  most  important  analyses  in  the  entire  range 
of  the  arithmetic  of  the  grammar-school  grades.  If  neglected,  or  badly  taught, 
it  seriously  deranges  the  work  of  the  teachers  of  more  advanced  grade?,  where 
it  must  be  so  frequently  applied.  If  the  teacher  will  present  it  immediately 
after,  and  then  in  connection  with.,  a  review  of  Analysis  C,  in  the  Fifth  Grade, 
and  dwell  particularly  upon  the  step  noted  in  parenthesis,  a  great  part  of  the 
difficulty  in  fixing  the  entire  process  will  disappear. 

7* 


154  SOW  TO  TEACH 

NOTE  2.— It  is,  of  course,  understood  that  the  examples  given  to  the  class 
will  not  be  confined  to  yards  and  dollars.  Even  the  order  of  these  should  be 
at  times  inverted  ;  as,  in  the  problem  last  treated,  we  might  have — 

If  $f  purchase  f  °f  a  yard,  how,  much  will  a  dollar  buy  ? 

SYLLABUS  OF  TOPICS  FOR  EXPANDED  REVIEW  OF  COMMON 
FRACTIONS. 

I.  Systematic  Review  of  Definitions  of  terms  used  in  fractions, 
with  illustrative  examples.  Omit  complex  fractions  having  fractions 
in  the  denominator.  Complex  fractions  having  an  integral  de- 

31 

nominator,  such  as  — !,  read  2^  fifths,  are  to  be  "  reduced  to  higher 
o 

terms."  See  AnalysisG,  page  152.  The  multiplier  to  be  used  is 
evidently  the  denominator  of  the  fraction  found  in  the  numerator. 
All  other  cases  of  "  complex  fractions,"  so  called,  should  be 

treated  as  indicated  division.      Such  expressions  as  -|  are  not 

JJ 

to  be  explained  as  fractions.  A  unit  cannot  be  divided  into  9| 
equal  parts. 

Examples  in  finding  the  Greatest  Common  Factor  of  numbers  by 
inspection. — Mental. 

Examples  where  the  factor  cannot  be  readily  found  by  inspec- 
tion, as  292  and  365 ; — 315  and  572.  The  SPECIAL  METHOD  re- 
quired is  too  difficult  for  analysis  in  this  grade.  It  is  one  of  the 
few  points  to  be  taught  empirically. 

The  result  always  should  be  tested  or  proved  in  accordance 
with  the  definition  of  Common  Factor  or  Common  Divisor. 

II.  Reduction  of  Fractions  to  their  Lowest  Terms. 

Examples  to  be  reduced  by  inspection  ;  HSo.  Mo,  Analysis  D, 
page  152. 

Examples  involving  the  special  method  of  finding  the  Greatest 
Common  Factor ;  as  fgl,  £ H,  etc.,  etc.  Not  too  long. — Analysis 
D,  page  152. 

Reduction  of  Improper  Fractions  and  Mixed  Numbers. 
1st.  Examples  solved  mentally  or  by  inspection. 
2d.  Examples  with  larger  numbers. — Analyses  A  and  B. 
Examples  in  finding  the  Least  Common  Multiple  of  two  or 
more  numbers — and  definition. 


ARITHMETIC.  155 

1st.  By  inspection,  as  5,  3,  2  ;  10,  20,  30. 

3d.  When  not  readily  solved  by  inspection,  as  28  and  39 ;  72, 
25,  88 ;  6, 12,  18,  24,  36,  and  48. 
Statement  of  Method  or  rule. 

Relation  of  Least  Common  Multiple  to  Least  Common  De- 
nominator. 

Distinguish  carefully  between  the  two,  and  define  each. 

Examples  in  reducing  to  Least  Common  Denominators. — 
Analysis  C. 

Give  occasional  examples  involving  preliminary  reduction  to 
lowest  terms  by  inspection. 

III.  Analysis  C.  Examples  in  Addition  of  Fractions  and  of 
Mixed  Numbers. 

Say  "  Reduce  to  Least  Common,  Denominator"  rather  than,  "Find 
tlie  Least  Common  Multiple  of  the  Denominators.  Of  course  the 
latter  forms  a  part  of  the  process  of  the  former. 

Examples  in  Subtraction  ;  as  -fa — A ;  87£ — 29^£.  Do  not  allow 
reduction  to  improper  fractions. 

Make  both  kinds  of  examples  as  practical  as  possible. 

Practical  Examples  (not  too  long),  each  involving  both  addition 
and  subtraction. 

NOTE. — Teachers  should  remember,  that  arithmetic  is  not  only  a  science, 
but  also  a  practical  art ;  that  this  art  involves  important  devices,  many,  or 
most,  of  which  have  been  already  taught,  and  their  principles  explained. 
These  devices,  such  as  reducing  to  lowest  terms,  cancellation,  rejecting  ter- 
minal O's  of  a  divisor,  should  not  be  at  any  time  lo*t  sight  of.  Examples 
should  be  occasionally  given  of  such  a  character  as  to  require  these  devices. 
The  omission  or  neglect  of  these  important  matters  would  be  a  serious  defect 
in  the  character  of  the  instruction  given. 

Principle  of  Cancellation. — Show  its  identity  with  dividing  by 
common  factors,  and  with  reducing  to  lowest  terms.  Show  this  by 
examples  in  fractions. 

Examples  of  simple  applications  of  cancellation  to  whole 
numbers. 

IV.  Multiplication  of  Fractions 

Give  examples  where  cancellation  cannot  be  applied. — 
Analysis  F. 

H  *  3-/y;  x  |f ;  ££x  144;  16|xl2|;  abstract  and  practical. 

Give  examples  that  should  be  done  by  cancellation. — Analysis. 
Lowest  terms. 


156  HOW  TO   TEACH 

125  x  A  5  It  of  $17.38  ;— if  39  barrels  cost  $84,  what  will  26 
barrels  cost  ? 

If  a  ton  of  hay  cost  $17£,  what  will  £$  ton  cost  ? 

If  1  acre  cost  $23f ,  what  will  19-,^  acres  cost  ? 

Pupils  should  be  made  familiar  with  the  following  principle 
and  its  applications.  It  is  frequently  the  most  convenient 
method  of  solution.  See  Analysis  E,  page  152.  i  of  a  number 
are  equal  to  |  of  3  times  the  number,  etc.,  etc. 

f  of  40  =  |  of  3  times  40. 

V.  Division  of  Fractions. 

1st  Review  and  apply  the  method  by  common  denominators. 

2d.  Review  thoroughly  its  analysis.    Analysis  G,  page  153. 

3d.  Teach  carefully  the  following  analysis,  giving  a  variety  of 
short  examples  to  fix  it  thoroughly.  See  Analysis  I,  page  157. 

4th.  Teach  the  brief  and  useful  device  of  inverting  the  divisor, 
but  in  no  case  let  the  analysis  of  the  rule  be  forgotten.  Let  it  be 
given  by  the  pupils  as  often  as  may  be  found  necessary  to  insure 
its  retention.  The  teacher  is  again  reminded  of  the  importance 
of  the  proper  application  of  the  principle  of  repetition  of  mental 
effort. 

Examples  in  finding  what  part  of  one  number  is  of  another; 
as  74  are  what  part  of  9£  ?  $4$,  what  part  of  $7$  ?  &  what 
part  of  f  f  ? — See  Analysis  I,  page  157. 

Give  examples  where  cancellation  cannot  be  applied  : 
H  -  ft ;  134  -  u. 

At  $1^  a  yard,  how  many  yards  can  be  bought  for  $134? 

If  5J  bushels  cost  $18},  what  will  1  bushel  cost? 

Give  examples  where  cancellation  is  to  be  applied  : 
234-s-Wr;  21J+2H,  etc. 

Give  short  examples  involving  simple  combinations  of  the 
multiplication  and  division  of  fractions ;  also  addition  or  sub- 
traction, with  multiplication  or  division,  like  the  following  : 

Bought  7|  yards  and  3£  yards  at  $1§  a  yard  ;  what  is  cost  of 
the  whole  ? 

Bought  36  yards ;  kept  9£  yards,  sold  the  remainder  at  $|  a 
yard  ;  how  much  did  I  get  for  it  ? 

If  I  had  sold  it  for  $74,  how  much  a  yard  would  that  be  ? 

If  $  yard  cost  $£,  what  will  -,a,  yard  cost  ? 

Iff  yard  cost  $7,  how  much  can  be  bought  for  $.1^  ? 


ARITHMETIC.  157 

POKMS  op  ANALYSIS. 

The  following  is  the  simplest  form  of  the  analysis  of  the  im- 
portant practical  rule  of  "  inverting  the  divisor,"  etc.  The  in- 
troductory step  of  using  a  unit  as  the  dividend,  is  only  a  case 
of  dividing  one  fraction  by  another. 

Analysis  I. — Example.— Divide  f  by  f. 

(Begin  with  a  unit  for  tlie  dividend,  and  apply  the  principle  of 
common  divisor.) 

1st  Step. — A  unit  divided  by  $,  or  ^  -=-  f  =  £  (which  quotient,  it 
will  be  observed,  is  the  divisor  inverted). 

3d  Step.-Therefore  f  of  a  unit  divided  by  ^  =  f  of  J  =  ££. 

Condensed  form.— (I  -s-  £)  =  ft  +§)  =  \ ;  therefore  (|  •*•  $)  =  f 
off=tt. 

Example.— If  f  of  a  yard  cost  $|,  how  much  can  be  bought  for 

f*f 

Analysis. — Combination  of  H  and  G.     Page  153. 
Example. — Iff  of  a  yard  cost  $f,  what  will  -ft  of  a  yard  cost? 
Combination  of  H  and  F. 

NOTE.— Give  a  thorough  review  of  analyses  F,  G,  and  H,  before  attempt- 
ing the  above  combinations. 


Decimal  Fractions. — The  exact  nature  of  decimal 
fractions  should  be  explained  and  illustrated ;  also  the 
meaning  of  the  word  decimal  Show  that  decimal  frac- 
tions  may  be  used  like  common  fractions  by  writing 
the  denominator.  Illustrate  by  the  decimal  notation, 
showing  that  whole  numbers  greater  than  9  are  also  ex- 
pressed decimally. 

Show  also  that  decimal  fractions  are  really  only  a 
kind  of  common  fractions,  the  two  having  the  relations 
of  species  and  genus.  The  methods  of  writing,  and  the 
various  analyses  are  essentially  identical,  case  for  case, 
as  shown  by  the  following  syllabus. 


158  SOW  TO  TEACH 

The  illustrations  may  embrace  the  following  : — 1. 
How  to  write  decimals,  as  7-tenths,  7-hundredths,  7- 
thousandths,  7-ten-thousaudths,  etc.  2.  Show  that  the 
numerator  is  FIRST  written,  as  in  common  fractions. 

3.  Show  that  the   "decimal  point"  and  the  ciphers, 
when  used,  are  only  required  to  indicate  the  denominator. 

4.  In  reading  decimal  fractions*  the  pupils  should  be 
cautioned  to  avoid  such  expressions  as  "  tens  of  thou- 
sands "  for  ten-thousandths,  "  hundreds  of  thousands  " 
for  hundred-thousandths,  etc.,  etc.    In  connection  with 
the  reading  of  such  fractions,  pupils  should  be  trained 
to  recognize  readily  the  comparative  value  of  diflferent 
fractions ;  as  that  .3  is  greater  than  .0987  or  .01  than 
.009596,  etc.    They  may  also  be  made  to  perceive  readily 
the   approximate  value  of  decimals  as  compared  with 
simple  common  fractions  ;  as,  that  .7634  is  a  little  more 
than  | ;  that  .8741  is  somewhat  less  than  £,  etc.     Pre- 
vious to  this,  however,  it  is  well  to  teach  the  exact  value 
of  certain  decimal    expressions:   as  .75=£,  .125  =  £, 
.375  —  4,  etc.     These  exercises  will  serve  to  render  the 

o » 

subsequent  work  of  the  pupil  intelligible. 

SYLLABCS  OF  TOPICS. 

I.  Exercises  in  READING  decimal  fractions. 

Exercises  in  telling  how  many  places  are  necessary  for  a  given 
denominator,  and  vice  versa. 

Exercises  in  writing  decimal  fractions. 

Reduction  of  decimal  fractions  : 

1st.  By  Inspection,  with  analysis  as  in  common  fractions. 

Examples,  mental,  oral,  and  written. 

.3  to  .OO's,  to  .OOO's,  etc. ;  .15  to  .OOOOO's.  To  higher  terms, 
Analysis  C,  common  fractions.  Page  152. 

3  to  .O's,  to  .OO's,  to  .OOO's,  etc. ;  7.8  to  .O's,  to  .OOO's,  etc. ;  to  im- 
proper fractions.  Analysis  A,  Page  152. 

Reduce. 700  to  lowest  DECIMAL  terms.  Give  Analysis  D,  Page  152. 


ARITHMETIC.  159 

NOTK.— Avoid  saying  "the  ciphers  to  the  right  are  crossed  off  because 
they  are  of  no  use."  The  statement  that  "  they  do  not  affect  the  value,"  is 
not  satisfactory  unless  the  pupils  show  why  they  do  not. 

II.  Reduce  common  fractions  to  decimal  fractions.  Give  Analy- 
sis E. 

Use  axiom— ^  of  a  unit  =  i  of  3  units ;  f  =  {  of  3. 

Make  this  definite  by  objective  illustration,  using  lines  divided 
into  parts. 

Example.— $  to  tenths ;  to  hundredths  ;  $  of  1  =  £  of  3  =  £  of  30 
tenths  =  7i  tenths  =  .7*  =  .75. 

NOTE.— Pupils  should  be  accustomed  to  read  decimal  fractions,  especially 
hundredths  (in  subsequent  grades  applied  to  per  cent),  so  as  to  include  out- 
standing fractional  parts,  where  there  are  any. 

It  is  generally  better  to  state  what  denominator  is  required,  instead  of  the 
more  indefinite  requirement  to  "reduce  to  a  decimal  fraction." 

Example.— Reduce  -,A,-  to  a  decimal  fraction  of  two  places,  or  reduce  fV 
to  hnndredths. 
Ans.  Two  places  will  give  hundredths  for  the  denominator. 

41  1  \4.GO 

—  =  —  of  4  =  —  of  four-hundred  hundredths  =  ll/ 

11      11  11  .36  4-11 

240                         240      24      3                                                             \3.00 
Reduce  —  to  a  decimal :  —  =  —  =-  =  ^  of  3  =  3^  of  300  hundredths  =4; 

320  320      32      4  .75 

Rule  1.  1st.  Reduce  the  numerator,  considered  as  a  whole 
number,  to  an  improper  fraction  with  the  required  denominator. 
2d,  Divide  by  the  given  denominator.  Or, 

Rule  2.  Divide  the  numerator  by  the  denominator.  . 

NOTE.— Give  examples  to  show  what  common  fractions  in  their  lowest 
terms  can  be  made  entirely  decimal,  and  which  can  not.  In  the  general  work 
of  the  class,  pupils  should  rarely  be  required  to  continue  the  division 
beyond  three  or  four  places. 

Reducing  Decimal  Fractions  to  Common  Fractions  in  their 
Lowest  Terms. 

Rule. — Write  the  fraction  as  a  common  fraction  and  reduce  to 
lowest  terms.     Analysis  D,  common  fractions. 
Examples:  .625    .4125     .87500    14.125 

.07|        .3Jr        .66|      5.114    .87* 

NOTE.— Pupils  should  be  made  thoroughly  familiar  by  rapid  mental  exer- 
cise, usually  without  analysis,  with  the  decimal  expressions  for  halves,  3ds, 
4ths.  5ths,  6ths,  7ths,  Stlis.  9t.hs,  llths,  12ths,  and  vice  versa,  using  preliminary 
reduction  to  lowest  terms  whenever  possible,  as  in  -fa,  §,  etc.,  etc. 


160  HOW  TO  TEACH 

III.    Addition  of  Decimal  Fractions. 

Examples:  Add  .2,  .05,  .008,  .7283.    Add  .0005,  .97  .0101,  etc. 
"  Give  mixed  numbers. 

Analysis  as  in  common  fractions,  by  principle  of  reducing  to 
lowest  terms.  The  necessary  additional  ciphers  may  be  "  under- 
stood "  in  the  solution,  but  not  in  the  oral  analysis,  which  should 
be  as  brief  as  possible. 

IV.  Subtraction  of  Decimal  Fractions. 

Examples  :    .1  —  .075 ;  1.001  -  .01009,  etc. 

Explain  as  in  common  fractions,  with  the  same  analysis. 

V.  Multiplication  of  Decimal  Fractions. 

NOTE. — Do  not  give  large  denominators.  Use  the  brief  rule  of  common 
fractions.  Cases  as  in  common  fractions. 

1st.  When  a  fraction  or  a  mixed  number  is  to  be  multiplied,  as  : 
4  times  .75,  17  times  8.047. 
Value  of  13  barrels  at  $8.375  a  barrel. 
2d.    When  a.  fractional  part  \»  to  be  taken,  as  : 
.4  of  .83,  .4  of  75,  .4  of  8.75. 

How  much  is  .7  of  $38.45  ?  .079  of  $120  ?  .90^  of  $160.48  ? 
Value  .17!»  of  ton  @  $92  a  ton  ?  at  $92.87^  a  ton  ? 
3d.    Combinations  of  the  1st  and  2d  cases,  as  : 
3.4  Ibs.  at  79  cts.  a  Ib.  ?  $.79  x  3.4. 
8  cwt.  75  Ibs.  @  $2.47  a  cwt.     $2.47  x  8.75. 

NofE.— As  preliminary  to2d  and  3d  cases,  give  mental  exercise?  in  finding 
thu  product  of  two  decimal  denominators,  as  "  lOths  by  JOths,  how  many 
places?  "  "  lOOOths  by  lOOths,  how  many  places  ?"  etc.,  etc. 

Examples  of  cases  involving  reduction  : 

.024  x  .15  =  ?  Product  of  numerators,  24  x  15  =  360,  the  new 
numerator,  lOOOths  by  lOOths  =  lOO.OOOths,  or  5  decimal  places 
for  denominator.  Am.  .00360  =  in  lowest  decimal  terms  .0036. 
Why  cross  off  the  last  0  ?  To  divide  both  terms  by  10. 

NOTE.— Many  questions  are  as  well  solved  by  the  application  of  principle 
(E)  in  common  fractions.  See  Analysis  E,  page  152. 

.079  of  $14.83=  .001  of  79  times  $14.83,  etc.,  etc. 

Use  or  not  as  may  be  judged  expedient. 

VI.  Division  of  Decimal  Fractions. 
There  are  two  cases,  as  in  common  fractions  : 


ARITHMETIC.  161 

1st.  When  the  divisor  is  an  integer  : 

7  -J-  8,  8  H-  7,  6H-5,  6  H-  120,  7.2  --  6,  3.6  -r- 120,  etc.    Put  ques- 
tion in  several  ways  :  1st,  Divide  7.2  by  6;  2d,  How  much  is 
£  part  of  7.2  ?    3d,  How  many  times  is  6  contained  in  7.2  ? 
etc..  etc. 

This  simple  case  does  not  require  the  principle  of  the  common 
denominator. 
2d.  When  the  divisor  is  or  contains  a  decimal  fraction  : 

6  H-.03 ;  .8  -r-  .005;  .004  -*-  .8;  .0036  -f-  .024;  7.2  •*-  .009;  8  -5-  5.45; 

3  -r-  7.203 ;  .2  -=-  8.75 ;  .3006  -f-  7.4 ;  8.5  -H  9.78 ;  8.638  -H  9.5 ;  8.638 

-j-  4.3,  etc.,  etc. 

Solution  and  analysis  by  the  principle  of  common  denominator. 

There  are  two  forms  of  applying  this  principle: 

1st.  Where  the  denominator  of  the  divisor  is  the  greater, 
(.003).6,)  INCREASE  the  denominator  of  the  dividend  to  .OOO's. 

2d.  Where  the  denominator  of  the  divisor  is  the  less,  (.12).  17286,) 
DIMINISH  the  denominator  of  the  dividend  to  .OO's  (hundredtbs) 
by  cutting  off  the  last  three  figures. 

A  General  Rule. — 1st.  Reduce  the  denominator  of  the  dividend 
to  the  denominator  of  the  divisor ;  2d,  Divide  the  numerator  of 
the  dividend  by  the  numerator  of  the  divisor. 

The  quotient  will  then  be  a  whole  number.  Other  decimal 
places  either  added  to  the  dividend  or  cut  off  from  it,  are  to  be 
"  brought  down  "  in  the  further  division,  and  will  give  the  frac- 
tional portion  of  the  quotient. 

Applications. — The  applications  of  decimal  fractions  will  be 
principally  found  in  Federal  Money.  Simple  combinations  with 
common  fractions  should  occasionally  be  used ;  also  simple  com- 
binations of  two  or  more  of  the  rules  of  decimal  fractions. 

Use  the  principles  of  cancellation  and  reduction  to  common  frac- 
tions whenever  they  will  simplify  the  operation. 

Examples  in  finding  what  decimal  fraction  one  decimal  fraction 
is  of  another  ;  especially  how  many  hundredths— use  ONLY  small 
amounts  or  very  simple  examples  : 

8  cents,  how  inany  hundredths  of  64  cents? 
$7.25,  how  many  hundredths  of  $9.75  ? 


162 


TEACH 


F  THE  FOURTH  GRADE. 

v  and  mutually  related  problems,  and 

imetic  of  the  higher  grades. 

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GEOGRAPHY.  103 


GEOGRAPHY. 

Geography  of  the  United  States  in  detail. — IN"  teach- 
ing the  geography  of  the  United  States,  it  is  particularly 
important  that  the  time  of  the  pupil  be  not  exclusively 
taken  up  with  the  study  of  mere  local  details — with 
learning  the  several  courses,  etc.,  of  long  lists  of  rivers, 
and  the  exact  situation  of  still  longer  lists  of  towns. 
A  certain,  but  carefully  limited,  amount  of  local  geo- 
graphy is  indispensable  as  a  basis  for  the  more  im- 
portant descriptive  geography. 

The  necessary  local  geography  embraces  the  names  of 
the  several  States  and  Territories,  and  their  division  into 
several  groups,  as  New  England,  Middle,  States  etc.,  etc.; 
their  boundaries  or  relative  positions;  their  important 
rivers,  lakes,  bays,  capes,  islands,  mountain  ranges,  and 
peaks ;  the  capital  of  each  State,  and  a  few  of  its  other 
leading  cities  or  towns,  if  of  any  importance.  All  these 
should  be  carefully  learned  as  a  basis  for  the  subsequent 
portions  of  the  study. 

The  descriptive  geography  should  include  the  simplest 
physical  outlines  of  the  country  as  a  whole ;  the  eleva- 
tions, the  great  mountain  ranges,  plateaux,  and  plains; 
the  drainage  by  single  rivers  on  the  Atlantic  slope,  and 
by  extensive  complex  river  systems  in  the  remainder  of 
the  country ;  the  climate,  with  its  modifications  in  the 
several  sections,  as  cold  or  hot,  wet  or  dry ;  the  leading 
industries  and  the  staple  agricultural,  mineral,  and 
manufactured  productions,  with  their  dependence  upon 
the  physical  conditions. 

Add  to  this  a  simple  and  very  brief  outline  of  the 
general  and  State  governments,  the  population,  its  four 
races  and  their  distribution;  the  great  commercial 


1G4  110 W  TO  TEACH 

routes,  natural  or  artificial,  and  the  cities,  as  the  centers 
of  manufacturing  and  commercial  industry. 

The  descriptive  geography  of  individual  States  or 
Territories  may  then,  in  great  part  at  least,  be  deduced 
from  a  consideration  of  these  general  facts.  All  tire- 
some sameness  and  repetitions  will  thus  be  avoided,  and 
the  pupil  will  be  made  to  appreciate  the  real  importance 
of  the  study. 

ELEMENTARY  SCIENCE. 

(By  Oral  Instruction.) 
BOTxlNY. 

THE  general  suggestions  relating  to  the  object  of  this 
branch  of  instruction,  given  in  connection  with  the 
subject  of  zoology,  in  the  preceding  grade,  and  the  re- 
marks there  made  in  regard  to  the  extent  of  classifica- 
tion, the  terms  employed,  etc.,  are  equally  applicable  to 
the  subject  of  botany.  As  a  science  of  observation,  this 
subject  has  a  decided  advantage  over  zoology,  especially 
for  educational  purposes,  inasmuch  as  the  objects  of 
which  it  treats  are  examined,  dissected,  and  analyzed 
with  more  facility.  They  also  possess  more  obvious 
beauty,  and  are  devoid  of  the  repulsiveness  which  at- 
taches to  so  many  objects  of  the  animal  kingdom.  An 
insect,  apparently  disgusting  at  the  first  view,  when 
closely  examined,  often  shows  more  beautiful  properties 
and  more  striking  evidences  of  design  than  the  most 
elegant  blossom ;  but  the  natural  aversion  to  handle  it, 
or  come  in  contact  with  it,  must  first  be  overcome. 

The  classification  of  plants,  being  based  upon  dis- 
tinctions often  very  minute,  must,  for  the  purposes  de- 
signed to  be  accomplished  in  these  simple  lessons,  be 


ELEVEN  TAR  Y  SCIENCE.  165 

carefully  limited.  Only  common  plants  need  to  be 
classified.  The  limitations  of  the  classification  to  be 
taught  are  indicated  below. 

The  first  few  lessons  should  show  the  structure  of 
plants  and  the  general  functions  of  each  of  their  parts, 
— the  root,  the  stern,  the  leaf,  the  flower,  the  seed  ;  the 
growth  of  the  plant  from  the  seed,  both  as  to  root  and 
stem,  the  food  of  plants,  buds  and  branches,-*-how  a 
plant  grows  from  them  ;  the  distinction  between  kerbs, 
shrubs,  and  trees  ;  also  between  annuals,  biennials,  and. 
perennials.  Examples  of  each  to  be  given. 

Classification  of  leaves — a  beautiful  and  very  useful 
department  of  the  subject,  especially  as  a  means  of 
training  the  powers  of  observation — may  then  be 
taught,  the  children  being  encouraged  to  gather  speci- 
mens for  careful  scrutiny.  The  vocabulary  employed 
to  indicate  the  peculiarities  is  very  interesting,  and  will 
serve  to  teach  something  of  etymology — as  ovate,  cordate, 
palmate,  digitate,  serrate,  etc.,  etc.  Give  the  pupils  for- 
mulce  for  methodical  examination  and  description. 
(See  Miss  Youmans's  "First  Boole  of  Botany.") 

Classification  of  roots  and  stems,  to  be  taught  in  a 
similar  manner,  but  much  more  briefly.  Next,  that  of 
blossoms.  First,  show  the  parts  of  a  blossom,  taking  a 
regular  one  to  begin  with — as  of  a  lily,  a  morning- 
glory,  or  a  butter-cup.  Analyze  so  that  the  pupils  can. 
see  the  parts,  showing  the  calyx  and  sepals,  the  corolla 
and  petals,  the  stamens  and  the  pistil  tvith  its  ovary. 
Give  a  sufficient  number  of  exercises  to  make  this  fami- 
liar, and  let  the  pupils  analyze  for  themselves.  The 
principal  forms  of  flowers,  as  bell-shaped,  wheel-shaped, 
salver-shaped,  cross-shaped,  butterfly-shaped,  etc.,  etc., 
may  then  be  shown.  The  arrangement  of  the  blossoms 
on  the  stem  (inflorescence),  as  far  as  it  can  be  exempli- 


166  HOW  TO  TEACH 

fied  by  actual  specimens,  as  head,  raceme,  spike,  umbel, 
etc.,  may  also  be  learned. 

The    following    outline    of    classification    may    be 
taught : — 

A.  (Series.)  Flowering  (ph&nogcmous)  plants. 

B.  (Series.)  Flowerless  (cryptogamous)  plants. 

At  first  use  only  the  familiar  terms.  The  scientific 
may  often  be  dispensed  with  entirely.  Give  examples 
of  plants  in  each  series ;  as — 

Rose.  Lily,  Geranium  ;  Fern,  Moss,  Mushroom. 

A,  including  a  (class).     Outside-growing  (exogenous) 

plants 

b  (class).     Inside-growing  (endogenous) 
plants. 

Illustrate  by  stems,  showing  the  rings  or  annual  lay- 
ers of  growth  in  the  former,  with  hark,  wood,  and  pith, 
and  their  absence  in  the  latter.  Teach  the  coincident 
peculiarities  of  the  leaves,  as  netted-veined  and  parallel- 
veined,  affording  a  ready  method  (approximate)  of  dis- 
tinguishing these  plants,  and  thus  giving  opportunity 
for  useful  exercises ;  also  those  of  the  seeds,  as  of  two 
seed  leaves  (cotyledons)  or  only  one  (dicotyledonous 
and  monocotyledonous). 

Familiar  examples  to  be  found  by  the  pupils ;  sucb 
as  Eose,  Buttercup,  Geranium,  Pea,  Potato,  Grape-vine, 
etc.,  etc.,  and  Lily,  Indian  Corn,  Common  Grass,  etc. 

(a),  Including  1.  Orders  or  families  of  plants,  with 
blossoms  of  many  petals  (polypetalous) ;  and,  2.  Orders, 
or  families,  of  those,  with  blossoms  of  one  petal  (rnono- 
petalous).  The  pupils  will  readily  find  specimens  of 
each,  the  names  of  which  they  have  already  learned. 

The  orders  of  (b)  should  not  be  taught.  Nor  need 
any  instruction  be  given  in  relation  to  the  classification 
of  cryptogamous  plants,  ferns,  mosses,  etc.,  this  being 


ELEMENT AE  Y  SCIENCE.  167 

too  difficult,  and  depending  upon  distinctions  not  suffi- 
ciently obvious  for  the  purpose  of  these  lessons.  Atten- 
tion, however,  may,  if  occasion  offers,  be  called  to  the 
fructification  of  ferns. 

Such  of  the  orders  or  families,  should  be  taught  as 
are  very  familiar,  and  depend  upon  quite  obvious  dis- 
tinctions, familiar  names  being  exclusively  used.  Thus 
the  Mustard  Family,  the  Pulse  Family,  the  Crowfoot 
Family,  the  Rose  Family,  the  Lily  Family,  etc.,  etc., 
may  be  taught  as  far  as  the  collection  and  presentation 
of  specimens  render  it  desirable  ;  that  is,  not  the  mere 
fact  that  there  are  such  families,  but  in  connection 
with  an  actual  object,  and  AV hen  the  inquiry  is,  to  what 
family  does  it  belong  ?  If  the  season  permits,  and  there 
is  an  opportunity  for  the  pupils  to  seek  for  specimens, 
'this  part  of  the  instruction  may  be  extended.  Here  the 
judgment  of  the  teacher  (never  to  be  superseded)  must 
be  carefully  exercised,  it  being  constantly  in  view  that 
the  object  of  these  lessons  is  not  to  make  the  pupils 
botanists,  but  to  create  a  basis  for  the  study  of  natural 
objects,  and  to  develop  the  faculties  of  perception  and 
reflection.  Species  need  not  be  taught,  although  the 
pupils  may,  as  occasion  offers,  be  made  to  perceive  the 
diversity  presented  by  different  individuals  of  the  same 
family,  so  as  to  learn  Avhat  is  meant  by  species. 

The  common  uses  of  plants  may  be  taught  to  some 
extent  incidentally  with  some  of  the  above  instruction, 
but  more  fully  at  this  stage.  This  will  embrace  their 
uses  for  food,  clothing,  medicine,  etc.  Take  our  own 
plants  first.  Show  that  the  roots  of  some  plants  are 
useful ;  of  others,  the  seeds  ;  others,  the  leaves;  others, 
the  fruit ;  others,  the  bark,  etc.  Some  few  plants  of 
other  climates  and  countries  may  then  be  referred  to, 
as  cotton,  rice,  sugar,  tea,  coffee,  etc.,  etc.  The  relation- 


168  HOW  TO  TEACH 

ship  of  these  plants  to  our  own  may  then  be  shoAvn; 
that  is,  the  families  to  which  they  belong. 


MINERALOGY. 

Before  commencing  instruction  in  this  branch,  the 
teacher  should  again  read  the  general  remarks  on  teach- 
ing elementary  science  in  the  Fifth  Grade.  This  sub- 
ject presents  some  peculiar  advantages  for  attaining  the 
special  object  of  oral  instruction — the  discipline  of  the 
observing  faculties.  In  no  other  department  of  natural 
science,  is  it  so  completely  within  the  power  of  the 
teacher  to  present  the  facts  to  be  acquired  to  the  im- 
mediate perception  of  the  pupils  in  the  class-room,  and 
in  no  other  is  more  delicacy  <>f  discrimination  required 
in  the  exercise  of  the  senses  upon  which  the  perceptions 
are  based.  But  while  the  objective  method  is  thus  seen 
to  be  peculiarly  applicable  to  this  branch  of  science,  it 
must,  at  the  same  time,  be  remembered  that  no  other 
subject  perhaps  requires  so  large  a  share  of  imparted 
information.  This,  however,  should  be  given  not  arbi- 
trarily, but  as  something  needed  to  supplement  the 
knowledge  gained  by  the  pupil  in  the  exercise  of  his 
own  faculties,  and,  as  far  as  possible,  in  answer  to  his 
inquiries,  the  determination  of  the  mind,  to  self-activity 
being  the  great  desideratum  in  this  kind  of  teaching; 
hence,  the  important  principle  should  be  kept  steadily 
in  view  that  nothing  should  be  done  for  the  pupil  which 
he  can  be  made  to  do  for  himself. 

The  teacher  should  also  bear  in  mind  that  it  is  utterly 
impossible  to  teach  the  subject  without  special  prepara- 
tion for  it — without  being  practically  familiar  with  at 
least  the  outline  facts  of  the  science.  This  preparation 
may  readily  be  made  with  the  assistance  of  even  a  small 


ELEMENTARY  SCIENCE.  169 

cabinet  of  minerals,  properly  labeled  (Day's  Grammar 
School  Cabinet,  for  example), .  and  any  of  the  smaller 
manuals  of  Mineralogy  (Dana's,  for  instance). 

What  has  been  said  in  the  preceding  grade,  as  to  the 
propriety  or  necessity  of  attempting  only  a  part  of  the 
subject,  is  equally  applicable  here.  What  is  done  should, 
however,  be  systematic — not  miscellaneous  and  unre- 
lated. Do  not  attempt  to  treat  any  of  the  topics  ex- 
haustively. A  large  part  would  not  be  understood  or 
remembered,  and  valuable  time  would  be  misapplied. 

The  investigations  made  by  the  pupils  in  relation  to 
each  mineral  should  be  guided  by  the  teacher  by  means 
of  a  regular  formula,  considering  in  a  fixed  order  its 
form,  structure,  cleavage,  fracture,  hardness,  weight, 
color,  luster,  etc  ,  etc.  These  special  characteristics  and 
their  proper  order  will  be  readily  remembered  after  a 
little  practice.  Each  term  thus  used  should  be  care- 
fully^llustrated  and  explained  as  soon  as  its  introduc- 
tion becomes  necessary. 

Begin  with  Minerals — Rocks  to  be  afterwards  con- 
sidered as  mineral  aggregates.  A  clear  conception  of 
the  general  properties  of  minerals  may  readily  be  given 
by  commencing  with  ice — water — steam. 

As  a  preparatory  step,  lead  the  pupil  to  form  some 
definite  idea  of  the  variety  of  forms  of  crystals,  by  briefly 
comparing  coarse  salt,  alum,  borax,  quartz,  mica,  rock- 
candy,  etc.  Use  only  the  term  crystal,  without  giving 
the  names  of  substances. 

In  treating  of  ice,  draw  attention,  not  by  telling,  but 
by  proper  questioning,  to  its  transparency,  color,  luster, 
weight,  solidity,  hardness,  fracture,  and  to  the  needle- 
like  crystals  which  can  be  so  readily  shown  in  ice-films 
when  water  begins  to  freeze,  and  in  the  frost-flowers  on 
the  window-pane.  Lead  him  now  to  see  that  a  block  of 
8 


HO  SOW  TO  TEACH 

ice,  or  a  snow  bank,  must  be  made  up  entirely  of  snch 
crystals,  even  though  their  individual  forms  are  no 
longer  perceptible.  Show  next  that  many  other  fluid 
substances,  like  water,  upon  losing  their  heat,  crystallize 
into  definite  solid  forms,  under  favorable  conditions,  as 
in  melted  sulphur,  and  in  the  beautiful  zinc  crystals 
which  cover  the  surface  of  so-called  galvanized  iron. 
Dwell  somewhat  upon  these  phenomena  of  crystalliza- 
tion, and  draw  attention  to  the  mysterious  and  inde- 
structible force  which  somehow  rebuilds  the  atoms  of 
the  water  into  the  same  forms,  no  matter  how  often  the 
ice  may  be  melted. 

The  next  step  in  this  preliminary  lesson  will  be  to 
show  that  crystals  may  also  be  formed  frgm  substances 
in  solution.  Alum,  salt,  borax,  etc.,  will  furnish  ready 
means  of  illustration.  Lead  the  pupil  further  to 
notice,  that,  as  in  the  case  of  the  ice,  so  with  the  sulphur, 
zinc,  alum,  etc.,  the  crystals  may  become  so  massed  as  to 
be  no  longer  individually  distinguishable. 

The  principal  points  to  be  fixed  in  such  a  lesson  are 
that  there  are  many  kinds  of  crystals,  some  formed  from 
liquids  which  have  become  solid  by  a  loss  of  heat,  and 
others  deposited  from  solution.  These  facts  will  be  found 
of  great  importance  in  further  treating  the  subject. 

The  pupil  is  then  prepared  to  compare  ice  with  a 
quartz  crystal,  which  should  be  presented  but  not  at 
first  named,  and  should  be  compared  first  as  to  the  re- 
semblances, then  the  differences.  When  the  pupils  can 
be  made  to  furnish  no  more  ideas,  the  teacher  should  state 
where  it  is  found,  its  relative  abundance,  geological  im- 
portance, economic  uses,  etc.,  etc.  Be  particular  not  to 
introduce  an  unexplained  term — such  as  the  name  of  any 
rock  or  mineral,  as  gneiss,  or  gypsum.  The  name  means 
nothing  until  explained  as  quartz  has  been.  Other  forms 


ELEMENTARY  SCIENCE.  171 

of  quartz  may  then  follow,  each  treated  in  the  same  way, 
and  each  in  its  turn  compared  with  those  that  have  pre- 
ceded it.  This  will  constitute  an  excellent  review,  and  will 
thoroughly  fix  what  has  been  already  taught.  Encour- 
age the  pupils  to  look  for  and  bring  in  specimens  which 
they  think  to  be  of  the  same  character  as  those  studied. 
Let  them  tell  why  they  think  they  are  the  same.  Let 
others  tell  why  they  think  they  are  not. 

Having  thus  treated  of  quartz,  next  consider,  in  the 
same  way,  feldspar  and  mica.  The  pupils  will  now  be 
ready  to  consider  a  rock. 

Let  it  be  gneiss  or  granite.  Let  the  pupils  look  for 
the  minerals  in  it  [a  cheap  single  lens  as  a  magnifier 
will  often  be  of  service].  Then  consider  the  texture, 
structure,  where  found,  uses,  etc.  The  mineral  horn- 
blende and  its  important  varieties  may  then  follow,  and 
after  that  the  rock  syenite. 

All  needful  information  may  be  obtained  from  any 
of  the  manuals  in  use. 

It  will  not  be  necessary  here  to  follow  out  in  detail  all 
the  minerals  and  rocks  of  which  it  is  desirable  that  pupils 
should  have  some  knowledge.  A  list  of  the  more  impor- 
tant, mostly  from  Dana,  is  subjoined,  from  which  the 
teacher  can  make  such  selections  as  will  conform  essenti- 
ally to  the  above  plan. 

MINERALS. 

Water;  carbon,  diamond,  coal  and  coal-mining,  an- 
thracite, bituminous,  jet,  plumbago,  amber,  petroleum, 
asphalt;  sulphur;  saltpeter,  salt,  borax  ;  lime,  gypsum, 
alabaster,  selenite,  calcite  spar,  chalk,  stalagmites,  lime- 
stones (crystalline  and  compact),  marbles,  quicklime, 
hydraulic  lime,  dolomite;  alum;  talc,  soap-stone. 
(French  chalk),  meerschaum,  pyroxene  and  hornblende. 


172  HOW  TO  TEACH 

corundum  and  emery,  feldspar,  albite,  orthoclase,  gar- 
net, mica. 

METALS. 

Mineralized  [ores]  or  native — Ores  of  tin,  iron, 
nickel,  zinc,  lead,  mercury,  copper,  gold,  silver,  plati- 
num. Enter  into  no  details  of  Metallurgy  ;  a  few  sim- 
ple facts  in  regard  to  smelting,  fluxes,  etc.,  will  not  be 
out  of  place.  The  economic  uses  of  these  metals  and 
the  poisonous  properties  of  some  of  them  should  receive 
very  careful  attention. 

KOCKS. 

As  single  minerals — example  pure  limestone.  As 
compounds — granite  or  conglomerate.  Eocks  as  crys- 
talline and  uncrystalline,  stratified  and  unstratified, 
aqueous,  igneous  and  metamorphic. 

The  relative  position  of  important  rocks — granite, 
syenite,  gneiss,  mica-slate,  steatite,  trap,  basalt,  lava, 
pumice,  slate,  shale,  schist,  quartz-rock,  burr-stone,  sand- 
stories,  grits,  conglomerates,  limestones,  marbles,  sand, 
clay. 

Such  of  these  rocks  as  are  found  in  the  vicinity  of  the  school, 
or  are  frequently  seen  by  the  pupils  when  used  for  paving,  flag- 
ging, building,  etc.,  should  receive  particular  attention. 

WRITING. 

Penmanship  and  Slate- Writing. —  Pen- 
manship should  be  carefully  taught  in  each  grade  of  the 
Course,  in  addition  to  the  constant  practice  which  is  re- 
quired in  ^late-writing.  By  means  of  the  latter,  if  a  due 
attention  is  given  to  it,  much  may  be  accomplished  in 
aiding  the  pupil  to  acquire  readiness  and  fluency  in  the 
exercise  of  this  art;  but  if  he  be  allowed  to  fall  into 


WRITING.  173 

careless  habits,  his  style  of  writing,  both  with  pen  and 
pencil,  will  be  almost  incurably  vitiated. 

The  exercises  in  spelling  from  dictation,  etc.,  should 
be  performed  with  punctilious  accuracy,  even  if  some 
sacrifice  of  rapidity  be  at  first  required.  Of  course,  there 
should  be  a  constant  effort  to  improve  both  in  rapidity 
and  accuracy — quantity  as  well  as  quality  being  made 
a  criterion  of  merit  and  success. 

The  slate-writing  should,  as  far  as  it  is  -practicable, 
exemplify  the  principles  and  methods  formally  taught  in 
the  lessons  in  Penmanship.  Pupils  should  not  be  per- 
mitted to  violate  in  the  one  class  of  exercises  the  rules 
and  precepts  taught  and  practiced  in  the  other.  This 
caution  is  especially  applicable  to  the  holding  of  the 
pencil,  which  should  be  sufficiently  long  to  be  held  as 
a  pen. 

The  lessons  in  penmanship  should  be  methodical  and 
progressive,  whatever  system  may  be  employed.  In  this, 
as  well  as  the  preceding  grade,  the  exercises  should  be 
rudimentary,  but  the  pupil  should  be  advanced  as  fast 
as  possible.  He  should  be  permitted  to  write  as  much 
as  is  practicable, —  making  strokes  and  curves  is  not 
writing,  although  it  may  be  valuable  as  leading  to  it. 
A  few  of  such  exercises  will  suffice. 

Neither  should  the  use  of  trial  papers  be  carried  to 
the  extreme  of  withholding  the  pupil  for  a  considerable 
time  from  the  use  of  his  copy-book,  so  that  months  are 
required  to  finish  the  latter.  The  pupil  should  be 
taught  the  necessity  of  doing  everything  as  well  as  he 
cando.it;  but  perfection  in  details  should  not  be  ex- 
pected in  the  rudimental  stages.  It  should,  from  the 
first,  be  deemed  essential  (at  least  meritorious}  to  exe- 
cute the  work  prescribed  with  dispatch,  provided  there 
is  no  want  of  care  or  attention.  Festina  lente,  however, 


IT4  HOW  TO  TEACH 

is  a  motto  that  applies  to  the  acquisition  of  this  art,  as 
(veil  as  others,  in  its  first  stages. 

A  proper  distinction  should  be  made  between  the 
lessons  given  to  show  the  pupils  how  to  write  and  the 
exercises  designed  to  practice  them  on  what  they  have 
thus  learned.  In  the  former,  the  whole  class  should 
invariably  be  occupied  in  the  same  work,  the  teacher 
explaining  and  illustrating  from  the  blackboard  the 
principles  and  methods  which  form  the  subject  of  the 
lesson  ;  in  the  latter,  practice  being  the  object  in  view, 
it  is  not  so  essential  that  nil  the  pupils  should  be  doing 
the  same  thing  at  the  same  time,  although  even  here 
it  is  a  convenience  to  the  teacher,  since  it  facilitates 
supervision. 

It  should  be  carefully  kept  in  view  that  the  hand  and 
the  eye  as  well  as  the  mind  of  the  pupil  are  to  be 
trained  in  this  branch  of  instruction, — the  hand  to  exe- 
cute, the  eye  to  discern,  the  mind  to  judge.  These  are 
not  to  be  educated  separately  and  successively,  but 
simultaneously.  The  pupil  must  be  taught  to  know 
what  is  the  correct  form  of  every  letter,  and  his  hand 
must  be  so  trained  by  correct  practice,  that  it  will  exe- 
cute the  dictates  of  mind  and  eye. 

Hence  a  correct  method  of  holding  the  pen,  a  proper 
position  of  the  body  while  sitting  at  the  writing-desk, 
and  a  suitable  placing  of  the  book  or  paper,  are  all  in- 
dispensable pre-requisites  to  the  acquisition  of  a  good 
hand-writing.  The  first  of  these  demands  especial  at- 
tention, and  every  lesson  should,  for  some  time,  be 
introduced  by  distinct  directions  as  to  the  proper  me- 
thod of  holding  the  pen,  and  these  the  pupils  'should 
not  be  permitted  to  violate.  With  regard  to  the  latter 
— position  of  body  and  position  of  book — a  few  simple 
directions  will  be  all  that  are  requisite. 


THIED    GEADE. 

OUTLINE    COUESE. 
Time  allowed,  from  eight  to  ten  moniln. 


LANGUAGE. 

Heading* — Of  the  grade  of  a  Fourth  Reader,  with  attention 
to  the  elocutionary  principles,  rules,  and  exercises  required  to 
teach  expression;  also  special  exercises  in  weal  culture. 

Spelling. — From  the  reading  lessons,  with  additional  exer- 
cises, both  oral  and  written  ;  careful  attention  to  syllabication. 

Definitions. — In  connection  with  the  reading  lessons;  also 
a  review  of  the  prefixes  and  suffixes  taught  in  the  preceding 
grade,  and  exercises  in  their  combination  with  various  easy 
roots. 

English  Grammar  and  Composition. —  Continued, 
with  the  analysis,  parsing,  and  construction  of  easy  complex  and 
compound  sentences ;  also  the  writing  of  short  compositions 
under  the  inspection  of  the  teacher. 


ARITHMETIC. 

Mental  Arithmetic. — Through  denominate  numbers  and 
fractions,  with  their  practical  applications  ;  also  a  review  of  the 
preceding  grades  by  exercises  in  both  calculation  and  analysis  ; 
and  a  careful  review  of  the  tables. 

Written  Arithmetic. — As  far  as  in  mental  arithmetic,  with 
similar  processes  and  methods  of  analysis;  also  with  exercises 
to  give  practical  expertness  in  simple  computation. 


176  HOW  TO  TEACH 


GEOGRAPHY  AND   HISTORY. 

Geography. — Of  South  America  arid  Europe,  both  local  and 
descriptive ;  the  topics  of  the  preceding  grades  to  be  occasion- 
ally reviewed  in  outline. 

History. — Of  the  United  States,  in  eluding  an  account  of  the 
early  discoveries,  and  the  outlines  of  the  Colonial  History  to 
1763,  only  such  dates  to  be  taught  as  are  essential  to  a  clear  un- 
derstanding of  the  narrative. 

ELEMENTARY  SCIENCE 

(FOR   ORAL  INSTRUCTION.) 

A  review,  as  far  as  possible,  of  the  topics  of  the  preceding 
grades,  and,  in  addition  thereto,  the  simple  outlines  of  Physio- 
logy and  Hygiene. 

WRITING. 

On  Slates. — Continued  as  in  the  preceding  grades. 

On  Paper. — "Words  containing  difficult  elementary  forms ; 
also  phrases  and  short  sentences.  Instruction  and  practice  in 
the  elementary  forms,  continued. 

DRAWING. 

Review  of  the  work  of  preceding  grades,  1o  which  add  scrolls, 
and  simple  geometrical  solids  in  outline,  such  as  the  cube  and 
parallelopiped,  in  various  positions;  also  the  cylinder,  cone,  pyra- 
mid, and  prism.  .  The  drawings  of  simple  objects,  domestic 
utensils,  etc.,  may  also,  occasionally,  be  copied  from  cards. 
Exercises  in  vinelike,  vertical,  and  horizontal  repetition  of  con- 
ventional forms,  and  in  drawing  designs  from  them,  may  now  be 
given. 


BEADING.  177 


How  TO  TEACH 


SUBJECTS     OF     T  H  K     T  II  I  K  1>    O  H  A  D  E. 


LANGUAGE. 

Heading. — In  the  preceding  grades,  due  attention 
is  required  to  be  given  to  emphasis  and  modulation; 
but  in  this  grade  the  exercises  should  take  the  special 
direction  indicated  by.  these  departments  of  elocution, 
so  as  to  lead  to  the  higher  stages  of  this  art,  required  in 
the  more  advanced  grades.  It  is  not  enough  that  the 
pupils  should  be  accustomed  to  read  with  clear  articu- 
lation and  proper  inflections  of  the  voice;  they  should 
be  taught  expression — to  comprehend  the  character  of 
the  piece  read,  to  enter  into  its  spirit,  and,  to  some  ex- 
tent, at  least,  communicate  it  justly  and  forcibly. 

Considerable  attention  should  also  be  given  to  vocal 
culture.  For  this  purpose  exercises  should  be  employed 
with  the  view  to  impart  the  physical  as  well  as  mental 
capabilities  required  for  this  purpose.  The  pupils  should 
be  taught  the  proper  position  of  the  body,  and  the  right 
mode  of  using  the  lungs  and  the  vocal  organs  so  as  to 
make  their  utterance  effective.  This  kind  of  discipline 
has  a  most  important  bearing  upon  the  general  physical 
development  of  the  pupils,  as  well  as  on  the  invigoration 
of  the  organs  specially  concerned  in  vocalization. 

For  the  attainment  of  the  special  objects  of  this 
grade,  the  elocutionary  rules,  principles,  and  exercises 
contained  in  the  Reader,  should  be  made  available  ;  a 


178  HOW  TO  TEACH 

portion  of  each  reading-lesson  being  devoted  to  this 
kind  of  instruction  and  practice. 

It  is  essential  that  the  pupils  should  be  required  to 
stand  while  engaged  in  these  exercises — either  the  whole 
class,  or  the  particular  pupil  called  upon  to  read.  The 
other  pupils,  in  a  proper  manner  and  in  the  right  spirit, 
may  be  permitted  to  criticise  the  performance  of  the  one 
called  upon  to  read,  and  to  exemplify  the  criticism  by 
reading  the  same  passage. 

Lessons,  especially  such  as  involve  a  difficulty,  should 
not  be  hurried  over ;  they  should  be  read  and  re-read, 
until  an  approximation,  at  least,  to  correctness  has 
been  attained  by  one  or  more  pupils. 

Concert  reading  and  declamation  may  be  resorted  to 
occasionally,  with  very  beneficial  results. 

Spelling. — Oral  spelling,  except  for  the  purpose  of 
teaching  syllabication,  should  be  discontinued.  The 
proper  division  of  Avords  into  syllables  is  an  important 
matter,  and  should  receive  due  attention.  In  this  con- 
nection the  correct  use  of  the  hyiriien  in  compounds 
should  be  taught,  and  the  pupils  exercised  therein. 

The  written  exercises  should  be  correctly  performed, 
with  care  not  only  as  to  penmanship,  but  as  to  capitals, 
punctuation,  etc.  These  exercises  should  be  carefully 
inspected,  and  after  the  errors  have  been  pointed  out, 
should  be  revised  and  corrected  by  the  pupil  himself.  The 
sentences  used  for  dictation  should  contain  a  sufficient 
number  of  common  test-words,  including  proper  names, 
both  of  persons  and  places,  so  as  to  impress  the  orthog- 
raphy of  such  terms  firmly  on  the  pupils'  minds. 

Definitions. — For  suggestions,  see  the  preceding 
grade. 


GRAMMAR.  179 

English  Grammar. — Analysis,  par  sing  &i\(\.  con- 
struction are  to  be  continued  in  this  grade,  the  class  of 
sentences  employed  being  of  a  more  difficult  character, 
but  still  carefully  kept  within  the  assigned  limits  of 
"easy  complex  and  compound  sentences." 

By  these  are  meant  such  as  involve:  1.  Complex  sen- 
tences, containing  simple  adjunct  clauses,  or  brief 
clauses  used  as  subjects,  objects,  or  attributes, — those 
containing  long  and  involved  or  intricate  phrases  being 
reserved  for  the  next  grade;  2.  Compound  sentences, 
formed  by  the  union  of  simple  clauses,  or  of  complex 
clauses,  such  as  those  above  described.  The  analysis 
should  be  sufficiently  minute,  to  keep  before  the  pupil's 
mind  the  relations  upon  which  grammatical  distinctions 
are  based.  The  simple-it  phraseology  should  be  used. 

The  exercises  in  construction  should  be  made  to 
correspond  with  the  advanced  character  of  the  analysis ; 
and  the  pupils,  in  the  "short  compositions"  required  to 
be  written,  should,  as  far  as  possible,  exemplify  the  in- 
struction in  the  other  portions  of  the  subject.  They 
should  be  required  to  analyze  and  parse  the  defective 
sentences  which  occur  in  their  own  compositions,  so  as  to 
discover  the  inaccuracies  and  to  afjly  the  necessary 
principles  and  rules  for  their  correction. 

The  exercises  for  the  special  purpose  of  accustoming 
the  pupils  to  care  and  criticism  in  the  use  of  language 
should  be  continued. 

Composition. — The  compositions  should,  as  far  as 
possible,  be  impromptu,  and  written  under  the  immediate 
inspection  of  the  teacher,  so  that  the  pupil  may  be  made 
to  depend  upon  himself  in  performing  what  is  required. 
Much  practice  of  this  kind  is  needed  before  the  formal 


180  HOW  TO  TEACH 

writing  of  compositions  is  assigned  as  a  home  task.  To 
many  pupils  this  very  essential  part  of  school  education 
is  made  utterly  repulsive  by  the  impossible  requirement 
that  they  should,  with  scarcely  any  previous  training, 
write  out  at  their  homes,  long  compositions  on  difficult 
themes  assigned  by  the  teacher. 

The  compositions  proper  for  this  grade  should  be 
brief,  and  on  simple  subjects,  which  should  be  either 
selected  by  the  pupils  themselves,  or,  when  prescribed 
by  the  teacher,  should  be  of  such  a  character  as  to  in- 
terest the  mind  of  a  child.  Those  which  require  the 
pupils  to  relate  the  incidents  of  their  own  experience — 
what  they  have  seen,  heard,  or  enjoyed,  are  chiefly  to 
be  preferred,  since  they  are  thus  required  to  make  use 
of  their  own  language,  while  their  attention  is  given 
rather  to  the  thought  than  to  the  expression.  And  this 
is  an  important  consideration;  for  exercises  of  this  kind 
should  not  be  designed  to  teach  the  use  of  language  sim- 
ply, but  language  as  the  vehicle  of  thought. 


AEITHMETIC. 

Mental  Arithmetic. — For  the  purpose  of  review, 
brief  examples  in  fractions,  both  common  and  decimal, 
should  be  employed,  both  as  a  test,  and  more  thoroughly 
to  fix  in  the  pupil's  mind  a  knowledge  of  the  principles 
and  applications  of  fractions  as  taught  in  the  preceding 
grades.  The  improvement  made  by  the  pupils  in  ac- 
curacy and  rapidity,  as  well  as  in  the  ready  application 
of  arithmetical  principles  to  particular  cases,  involving 
an  exercise  of  the  judgment  and  reasoning  powers, 
should  be  progressive  from  grade  to  grade,  and  there- 
fore should  be  carefully  tested  in  the  mental  work. 


ARITHMETIC,  181 

The  special  province  of  this  grade  being  Denominate 
Numbers,  the  exercises,  both  in  mental  and  written 
arithmetic,  should  deal  largely  with  the  applications  of 
fractions  to  that  class  of  numbers,  including  Fed- 
eral money,  and  should,  of  course,  combine  practice  in 
all  the  essential  tables  of  weight,  measure,  etc. 

The  teacher  need  not,  perhaps  should  not,  conform 
himself  to  the  order  or  kind  of  examples  presented  by 
any  particular  text-book.  If  the  questions  given  out  to 
the  pupils  to  be  solved  instanter  are  spontaneously  con- 
structed by  the  teacher,  they  will  be  more  appropriate 
to  the  special  needs  of  the  pupils,  and  the  exercise  will 
have  fur  more  spirit,  and  be  of  much  greater  value.  It  is 
among  the  dullest  of  all  the  occupations  of  the  class- 
room to  read  from  a  book  questions  in  mental  arithme- 
tic, of  little  variety,  hackneyed  in  form  and  character, 
and  which  the  pupils  have  previously  been  required  to 
con  over.  To  expect  an  uninterested,  drowsy  class  to 
perform  any  intellectual  exercise,  is  absurd;  but  the 
absurdity  is  greater,  perhaps,  in  mental  arithmetic  than 
in  any  other  subject.  For  suggestions  in  relation  to 
this  point  the  teacher  is  referred  to  the  statements  made 
under  the  fifth  grade. 

The  review  of  the  analysis  previously  taught  should 
be  systematic  and  thorough,  but  should  not  consume  a 
large  part  of  the  time  of  the  pupils. 

Written  Arithmetic. — The  arithmetic  specially 
prescribed  in  this  grade,  both  mental  and  written,  is 
of  a  practical  character,  perhaps  more  generally  so  than 
in  any  other  grade  of  the  course.  All  that  precedes 
has  been,  to  a  considerable  extent,  a  preparation  for  the 
work  of  this  grade,  and  will  be  found  involved  in  it. 

The  whole  subject  of  compound  denominate  numbers 


182  HOW  TO  TEACH 

is  strictly  utilitarian.  Practical  utility  should,  there- 
fore, be  the  controlling  element  in  all  the  exercises  em- 
ployed. The  daily  necessities  of  th.e  house,  the  shop,  the 
market,  etc.,  indicate  the  general  character  of  the  selec- 
tions to  be  made.  These  will  furnish  at  least  as  good 
mental  discipline  in  calculation  and  analysis  as  those  of 
a  less  severely  practical  character. 

It  is  usually  the  case,  that  pupils  who  have  reached 
this  grade  can  spend  but  little  more  time  in  school.  In 
view  of  this  fact  it  is  important  to  attend  first  to  the 
more  practical,  and  therefore  more  essential,  parts  of  the 
arithmetic  of  the  grade.  To  this  end,  the  tables,  its  in- 
dispensable basis,  should  be/thoroughly  reviewed,  and  not 
only  memorized,  but  understood.  Pupils  should  be 
trained  to  work  with  reasonable  rapidity,  and  all  long 
and  complex  examples,  as  well  as  those  involving  ob- 
solete weights,  measures,  or  money,  should  be  care- 
fully avoided.  Reduction  should  not  be  so  long  dwelt 
upon  as  to  lead  to  the  omission  of  important  practical 
points  in  other  rules.  It  is  desirable  that  a  record  of 
the  points  covered  by  the  class-work  should  be  method- 
ically kept  to  be  used  as  a  basis  of  the  necessary  re- 
views. 

SYLLABUS. 

Reduction  Descending. — Show  why  it  is  so  called.  The 
denominations  should  always  be  written  with  the  exarn^ 
Pupils  should  not  be  allowed  to  "  add  in"  by  a  separate  line; 
it  greatly  increases  the  work,  absorbs  the  time  unprofitably,  and 
indicates  mental  feebleness.  The  explanation  or  analysis  should 
be  given  by  processes  which  make  the  multiplier  an  abstract 
number.  The  impossibility  of  multiplying  by  a  concrete  number 
should  be  carefully  shown. 

As  an  illustration  of  the  above,  suppose  the  question  to  be, 


•   ARITHMETIC.  183 

"  How  many  pints  in  75  gallons,  3  quarts  ?  "    There  are  at  least 
two  correct  methods  of  analysis  for  this  question. 

Analysis  1. — Since  4  quarts  make  1  gallon  there  are  4  times  as 

gals.         qts.     many  quarts  as  there  are  gallons  (75),  which  are 

75  3      300    quarts  ;    300    quarts  and  3  quarts  are  303 

quarts  ;  and  since  2  pints  make  1  quart,  there  are 

605  qts.  twice  as   many  pints  as  there  are  quarts  (303), 

606  pts.  which  are  606  pints. 

In  this  analysis  the  work  done  on  the  slates  is  directly  ex- 
plained, the  multipliers  4  and  2  used  in  the  slate-work  and  in  the 
analysis  being  identical. 

Analysis  2. — Since  in  1  gallon  there  are  4  quarts,  in  75  gallons 
there  are  75  times  4  quarts,  which  are  300  quarts ;  300  quarts  and 
3  quarts  are  303  quarts  ;  and  since  in  1  quart  there  are  2  pints, 
in  303  quarts  there  are  303  times  2  pints,  which  are  606  pints. 

In  this  analysis,  which  is  concise,  and  perhaps  more  clear 
than  the  other,  the  work  done  on  the  slate  is  indirectly  ex- 
plained, the  multipliers  75  and  303  not  being  those  actually 
used.  When  this  method  is  employed,  an  illustration  of  the 
following  principle  should  be  occasionally  required  :  "  The  prod- 
uct of  two  or  more  abstract  numbers  is  the  same,  whatever 
may  be  the  order  of  the  factors."  Also  the  modification  of  this 
principle,  in  the  case  where  one  of  the  numbers,  as  in  the  given 
instance,  is  concrete. 

The  following  errors  are  frequently  heard  and  should  be 
avoided  :  "  I  multiply  75  gallons  by  4  quarts,  etc."  Four  quarts 
times  75  gallons  is,  of  course,  absurd. 

I  multiply  75  gallons  by  4,  etc.  Pour  times  75  gallons  is  of 
course  300  gallons,  not  300  quarts. 

It  will  be  seen  that  the  above  analyses  and  that  required  for 
Reduction  Ascending  are  identical  with  those  already  given  in 
the  preceding  grades.  The  "  adding  in  "is  the  same  as  in  the 
reduction  of  mixed  numbers. 

Reduction  Ascending.— This  is  best  taught  and  under- 
stood in  immediate  connection  with  Reduction  Descending,  at 
first  by  reviewing  the  same  example.  Long  division  by  divisors 
less  than  13  should  not  be  allowed,  nor  if  catting  off  O's  will 
change  to  short  division. 


184  HOW  TO  -TEACH 

Explanation  may  be  by  any  process  which  will  clearly  ac- 
count for  the  denominations  of  the  successive  quotients  and  re- 
mainders. 

Weights. — Teach  briefly  by  examples  the  relations  of  Avoirdu- 
pois and  Troy  weights,  and  the  essential  identity  of  Troy  and 
Apothecaries'  weights.  Let  most  of  Ihe  examples  in  Reduction 
be  in  the  first  of  the  three.  They  ghoiiKi  be  few  and  very  short 
in  the  last. 

Remember  that  the  quarter  of  a  hundredweight  is  seldom 
used  now,  excepting  in  text-books — the  Avoirdupois  dram  no- 
where else. 

lu  addition  and  subtraction,  give  only  Avoirdupois  weight. 
Remember  that' in  things  sold  by  the  ton,  the  ounce  is  not  taken 
into  account.  Review  the  principle  of  carrying,  if  that  plan 
is  used  ;  of  its  better  substitute,  if  not.  A  short  question  in  Troy 
weight  may  be  written  upon  the  board  or  read  from  the  text- 
book if  pupils  have  one.  Then  require  them  to  state  succinctly 
what  process  will  be  required  in  working  it,  omitting  detailed 
analysis. 

NOTE.— To  avoid  repetition,  it,  may  here  be  stated,  that  the  plan  jupt  men- 
tioned may  be  taken  in  multiplication  and  division  as  well  as  in  reduction, 
addition,  and  subtraction,  with  those  portions  of  the  weights,  measures1, 
etc.,  practice  in  which  is  of  less  general  utility.  Many  practical  examples  in 
multiplication  and  division  will  arise  under  Avoirdupois  weight,  such  as 
finding  values  at  so  much  a  pound,  hundredweight  or  ton,  or  vice  versa.  Such 
examples  may  involve  preliminary  addition  or  subtraction,  or  both, 

Linear  Measure.  —  Reduction.  —  Employ  the  denominations 
most  in  use — the  inch,  the  foot,  the  yard,  the  rod,  and  the  mile 
— very  rarely,  if  ever,  all  in  the  same  example.  Omit  cloth 
measure,  or  if  briefly  referred  to,  use  only  ^s,  ^s,  £ths  and  i^ths. 
Give  a  very  few  examples  to  show  the  use  of  the  chain  and  its 
subdivisions.  Measuring-tapes  usually  have  feet  on  one  side  and 
chains  and  links  on  the  other.  One  may  be  employed  to  advan- 
tage in  the  class-room.  To  convert  feet  or  yards  into  miles,  and 
vice  versa,  use  only  5,280  and  1,760;  for  instance,  so  many  miles 
of  railroad  track  having  so  many  Ibs.  of  iron  to  the  yard,  at  so 
much  a  ton,  etc.,  etc.  Omit  addition  and  subtraction,  multipli- 
cation and  division. 

Surface  Measure. — (Of  very  great  practical  importance.) — Treat 
briefly  in  reduction.  When  8Q\  is  used  as  a  divisor  let  it  be  in 
very  short  examples.  Give  examples  in  addition  and  subtrac- 


ARITHMETIC.  185 

tion.  In  multiplication  and  division  give  examples  in  finding 
areas  of  rectangular  figures,  in  feet,  in  yards,  etc.  Give  the  feet, 
or  the  chains,  on  the  sides  of  rectangles,  to  find  acres  and  value ; 
acres  and  hundredths  the  most  usual  form.  Omit  roods.  Sim- 
ple questions  may  be  given  occasionally,  involving  cost,  in  esti- 
mating for  plastering,  bricks,  carpets,  dress-linings,  etc. ;  also 
very  simple  questions  in  finding  the  area,  circumference,  or  di- 
ameter of  a  circle  when  square  root  is  not  involved,  using  ff  or 
3.1416  for  ratio. 

Solid  Measure. — Employ  only  the  inch,  the  foot,  the  yard,  and 
the  cord  ;  use  the  last  but  little.  See  that  pupils  understand  the 
mutual  relations  of  linear,  surface,  and  solid  measures,  and  that 
they  are  not  convertible,  the  units  being  of  totally  different  na- 
tures. Reduction — a  few  simple  questions.  Omit  addition  and 
subtraction.  Give  examples  in  finding  cubic  inches,  feet,  or 
yards,  in  boxes,  bins,  cellars,  cylindrical  cisterns,  etc.,  etc. 
Some  knowledge  onboard  measure,  giving  very  simple  practical 
examples  involving  cost. 

Dry  and  Liquid  Measures. — Use  no  obsolete  denominations. 
Omit  beer  measure.  Remember  that  the  barrel  and  the  hogs- 
head are  not  often  measures  in  commerce.  Simple  examples  in 
reduction.  Omit  addition  *and  subtraction.  Give  the  simplest 
possible  examples,  in  connection  with  solid  measure,  in  finding 
bushels  or  gallons  in  bins,  vats,  cisterns,  etc.,  using  281  and 
2150  cubic  inches,  and  omitting  fractions.  No  other  multiplica- 
tion or  division  should  be  required. 

Circular  Measure. — Treat  briefly ;  explain  the  terms  and  their 
use ;  omit  signs.  Reduction — Short  examples  of  two  or  three 
terms.  Addition  and  Subtraction  — Questions  in  difference  of 
latitude  and  longitude.  Geographical  and  statute  miles  on  the 
meridian,  on  the  equator,  on  parallels  of  60°. 

Time. — (In  part  very  important.)  Treat  reductions  very 
briefly.  Do  not  involve  more  than  two  or  three  denominations 
in  one  example.  Leap-year.  Addition  and  subtraction.  Dif- 
ference of  dates — by  days,  and  by  years,  months  and  days.  Re- 
lations of  difference  of  longitudes  to  time.  Explanations  and 
examples.  Conversion  of  longitude  into  time  and  vice  versa. 

Miscellaneous. — Practical  examples  in  values,  involving  dozen, 
gross,  quire,  ream,  quintal,  barrels  of  flour,  tiah,  etc.,  making 
out  simple  bills,  receipts,  etc. 


186  HOW  TO  TEACH 

Money. — Reduction  and  other  simple  exercises  in  Federal 
money  are  always  in  order  from  the  Fifth  Grade.  Give  but 
few  examples  in  each  rule  in  sterling  money.  Reduction  of 
sterling  to  Federal  and  vice  versa,  omitting,  of  course,  all  refer- 
ence to  the  percentage  of  exchange. 

Pupils  should  know  something  of  the  money  of  Canada — 
identical  with  our  own — the  value  of  the  franc,  and  of  the 
German  mark. 

Fractional  Compound  Numbers. — The  consideration  of  this  sub- 
ject has  been  deferred  to  avoid  complicating  it  with  simpler  and 
more  important  matters.  Reject  all  examples  in  addition,  sub- 
traction, multiplication,  and  division.  In  reduction  there  are 
but  two  cases,  and  the  second  of  these  is  simply  the  converse  of 
the  first.  Each  divides  into  two  varieties,  in  one  of  which  the 
fraction  is  common  and  in  the  other  decimal,  but  the  principle 
applied  in  working  is  the  same. 

Be  careful  to  select  only  those  denominate  numbers  in  which 
such  fractional  quantities  are  likely  to  need  consideration,  chiefly 
sterling  money. 

I  A.  f£  of  a  bushel  to  pecks,  quarts,  etc. 

Examples  :  Case  1st.  -J  B.  . 673  of  a  £,  how  many  shillings,  pence, 
/  etc.,  or  dollars  and  cents. 

f  A.  7ft.  95  in.,  what  common  fraction  of  a 

cubic  yard  ? 

„  n  „„  0  j      B.  15  cwt.  38  Ibs.  are  what  decimal  frac- 

tion of  a  ton? 

£8  14s.  9.^1  are  how  many  dollars  and 
L  cents  (at  $4.866i)  ? 

GEOGRAPHY. 

SOUTH    AMERICA. 

Local  GeograpJt/t/. — Begin  with  the  continent  of 
South  America,  as  a  whole,  its  boundaries,  the  names 
and  relative  positions,  or  boundaries,  of  its  political 
divisions — a  few  of  the  chief  capes  and  islands,  the  posi- 
tion and  direction  of  the  great  plateaux  and  mountain 
ranges  [use  chalk  sections  roughly  drawn  on  blackboard] 
— five  or  six  of  the  most  famous  volcanoes.  In  the 


GEOGRAPHY.  187 

drainage,  only  two  or  three  lakes,  the  courses  of  the 
Orinoco,  the  Amazon,  the  San  Francisco,  and  the  Pa- 
rana described,  and  their  great  branches  named  and 
pointed  out  as  systems,  but  not  described. 

The  local  geography  of  the  several  countries  taken 
separately  should  be  very  brief,  and  should  include  a 
review  of  the  matter  previously  considered  in  the  study 
of  the  continent — that  is,  the  relative  positions  or 
boundaries,  the  positions  of  the  mountains  and  pla- 
teaux, the  principal  rivers,  etc.,  etc.,  together  with  the 
capitals  of  the,several  countries,  and  about  twenty-five 
of  the  other  principal  interior  cities  and  seaports  of  the 
continent. 

Descriptive  Geography. — It  will  also  be  found 
most  expeditious  and  effective  to  teach  the  descriptive 
geography  of  the  continent  first  as  a  whole.  From 
this,  that  of  the  several  countries  may  be  very  easily 
deduced  and  distinctly  remembered.  It  should  include 
the  surface  of  the  country  as  mountain,  plateau,  or 
plain;  the  zones;  the  climate  as  modified  by  latitude, 
elevation,  and  the  prevalent  winds;  the  leading  char- 
acteristics of  the  great  plains  and  plateaux  ;  a  brief  no- 
tice of  volcanoes  and  earthquakes  ;  a  few  of  the  princi- 
pal plants  and  animals;  the  three  races,  their  distribu- 
tion, and  their  principal  occupations,  and  the  influence 
of  the  physical  geography  thereon  ;  the  European  lan- 
guages spoken ;  the  chief  productions  and  exports,  vege- 
table, animal,  and  mineral,  and  the  forms  of  govern- 
ment. 

EUROPE. 

Local  Geography. — The  geography  of  Europe 
should  be  so  taught  as  to  avoid  the  presentation  of  a 


188  HOW  TO  TEACH 

large  amount  of  minute  detail.  In  local  geography  the 
boundaries  of  the  continent,  the  names  and  relative  po- 
sitions or  boundaries  of  its  states;  the  position  of  its 
principal  peninsulas, capes,  gulfs,  bays, seas,  and  straits; 
its  chief  highlands  and  lowlands;  from  twelve  to  fifteen 
principal  mountain  systems,  the  famous  volcanoes,  the 
great  islands  and  groups  of  islands,  seven  or  eight  im- 
portant lakes,  including  two  or  three  in  Switzerland ; 
from  twenty  to  twenty-five  of  the  important  rivers,  spe- 
cifying those  which  are  important  as  commercial  water- 
ways ;  the  names  and  positions  of  the  capitals  of  the 
several  countries,  and  from  fifty  to  seventy  of  the  other 
important  cities. 

Descriptive  Geography. — The  descriptive  ge- 
ography to  be  on  the  same  plan  as  for  North  and  South 
America.  It  should  include  the  general  surface,  climate, 
and  productions,  the  people  and  their  industries,  to- 
gether with  their  relations  of  blood,  language,  com- 
merce, etc.,  with  the  people  of  the  United  States.  In 
reviewing  the  chief  cities,  state  any  important  or  inter- 
esting facts  in  relation  to  each. 

Iteview. — The  topics  of  the  preceding  grades  should 
now  be  reviewed  in  outline. 

This  important  requirement  may  best  be  met  by  mak- 
ing the  exercise  a  comparative  one.  It  should  not  be  a 
home-lesson,  but  a  vigorous  class-room  exercise,  dis- 
carding for  the  time  the  text-book,  and  using  the  out- 
line maps,  the  pointer,  and  the  globe.  For  instance,  a 
rapid  pointing  out  and  naming  of  all  the  countries  of 
America  and  Europe,  ai)d  their  capitals,  might  consti- 
tute one  lesson;  all  the  mountain  systems,  plateaux, 
plains,  and  volcanoes,  another ;  the  climate  and  produc- 
tions, a  third ;  and  so  on. 


HISTORY.  189 

HISTORY  OF  THE  UNITED  STATES. 

General  Suggestions. — The  leading  purpose  of 
this  study  is  that  the  pupil  may  understand  the  origin, 
character,  and  condition  of  the  nation  of  which  he  is  a 
part,  and  that  lie  may  be  fitted  for  an  intelligent  exercise 
of  his  duties  and  responsibilities  as  a  citizen, 

It  is  obviously  impossible  to  treat  so  comprehensive  a 
subject  exhaustively.  The  immaturity  of  the  pupil's 
mind  and  the  pressure  of  other  studies  alike  forbid. 
Yet  the  leading  facts  and  principles  may  be  readily 
comprehended  and  remembered,  and  the  outline  which 
he  is  to  retain  be  made  from  the  first  coherent  and  defi- 
nite. To  this  end  a  simple  preliminary  outline  sketch 
should  be  carefully  fixed  in  the  minds  of  the  pupils  of 
this  grade,  and  frequently  reverted  to  in  the  reviews  of 
all  the  grades  in  which  the  subject  is  taught.  The  ge- 
ography already  learned  will  greatly  simplify  the  process. 
This  outline  can  be  given  most  expeditiously  and  effi- 
ciently by  means  of  oral  instruction  and  the  use  of  the 
map.  It  should  be  very  brief,  and,  if  it  be  thought  ex- 
pedient, should  be  reduced  to  writing  by  the  pupil  for 
reference.  All  detail  should  be  reserved  for  the  study 
of  the  text-book. 

The  following  sketch  is  presented  only  as  illustrative 
of  this  suggestion.  Its  modification  byre-arrangement 
or  otherwise,  or  the  substitution  of  another  in  its  place, 
may  be  found  desirable. 

OUTLINE  SKETCH. 

1st.  The  people  of  the  United  States  are  of  European  descent, 
excepting  the  negroes. 

2d.  Less  than  400  years  ago  our  ancestors  knew  nothing  of 
the  existence  of  this  continent. 


190  HOW  TO  TEACH 

3d.  Spain,  guided  by  Italian  genius,  led  the  way  to  its  discov- 
ery, exploration,  and  colonization. 

4th.  The  first  permanent  English  settlement  within  our  limits 
was  not  effected  until  more  than  a  century  after  the  voyage  of 
Columbus.  In  the  interval,  Spain  and  Portugal  had  possessed 
themselves  of  the  shores  and  islands  of  the  Mexican  Gulf  and  of 
nearly  all  South  America. 

5th.  For  a  century  and  a  half  the  English  colonies  were  con- 
fined to  a  narrow  strip  east  of  the  Alleghauies. 

6th.  Spanish  slavery  exterminated  the  Indians  of  the  West 
Indies.  This  led  directly  to  the  opening  of  the  African  slave 
trade,  and  indirectly  to  the  introduction  of  slaves  into  our  own 
country. 

7th.  The  colonies  had  wars  with  the  Indians  m  whose  coun- 
try they  had  settled,  and  with  the  neighboring  French  colonies. 
The  French  were  subjugated  and  their  territories  occupied. 

8th.  Less  than  a  century  ago  all  European  settlements  were 
still  dependent  colonies. 

9th.  The  necessities  of  distant  colonial  settlements  had  de- 
veloped in  the  English  colonies  a  spirit  of  self-reliance  and  po- 
litical freedom,  and  a  system  of  local  and  elective  self-govern- 
ment. 

10 th.  The  expenses  of  the  French  wars  left  a  heavy  debt  and 
led  to  unusual  taxation.  A  tyrannical  system  of  taxation  led  to 
the  War  of  Independence,  which  fixed  the  national  boundary 
at  the  Mississippi.  The  colonies  had  become  States. 

llth.  The  present  form  of  government  (the  Constitution)  was 
established  soon  after  the  close  of  the  war,  about  eighty-three 
years  ago. 

12th.  The  number  of  States  has  been  greatly  increased  by  im- 
migration and  emigration.  The  population  and  wealth  have 
increased  many  fold. 

13th.  By  purchase  and  otherwise  the  national  territory  has 
been  expanded  to  the  Gulf  of  Mexico  and  to  the  Pacific  and 
Arctic  oceans. 

14th.  Since  the  War  of  Independence  there  have  been  three 
important  wars  :  1.  A  war  with  England'in  defense  of  naturalized 
citizens  and  in  vindication  of  the  rights  of  neutrals  ;  2.  A  war 
with  Mexico,  resulting  from  our  annexation  of  Texas;  3.  A  great 


HISTORY.  191 

civil  war,  arising  in  part  from  questions  originating  in  our  colo- 
nial history  and  in  part  from  more  recent  causes. 

Lessons  and  Recitations. — Lessons  in  history  should 
be  assigned  by  topics  and  not  by  pages. 

All  verbatim  recitations  of  sentences  and  paragraphs 
should  be  strictly  forbidden,  and  the  pupils  should  be 
required  to  state  the  facts  in  their  own  language. 

Only  such  dates  should  be  committed  to  memory  as 
are  indispensable  as  landmarks  in  history.  The  se- 
quence of  events,  rather  than  the  precise  date  of  each, 
is  what  is  chiefly  necessary. 

Maps,  especially  those  of  the  text-books,  snould  be 
used  whenever  the  subject  may  require  it. 

Historic  episodes,  however  interesting,  should  not  re- 
ceive the  careful  study  given  to  the  essential  narrative. 
The  stories  of  Juan  Ponce  de  Leon,  the  Conquest  of 
Mexico,  De  Soto's  Expedition,  John  Smith,  Pocahontas, 
the  Salem  Witchcraft,  etc.,  should  indeed  be  carefully 
read,  and,  as  far  as  may  be  necessary,  explained;  but, 
unless  great  care  be  taken  by  the  teacher,  the  pupils  will 
be  apt  to  conceive  that  these  are  the  most  important 
portions  of  the  history. 

Important  incidental  allusions  to  European  history, 
such  as  the  rise  of  the  English  Puritans,  the  expulsion 
of  the  Stuarts,  the  French  Revolution,  etc.,  should  be 
carefully  but  briefly  explained.  Great  caution  should 
be  exercised  throughout  these  lessons  to  state  the  facts 
in  such  a  manner  as  not  to  wound  the  religious  or 
political  sensibilities  of  any. 

Reviews. — Reviews  of  the  portion  already  taught, 
with  frequent  references  to  the  preliminary  sketch,  are 
of  the  highest  importance.  These  reviews  should  take 
three  distinct  forms:  the  Chronological,  the  method 


192  HOW  TO  TEACH 

usually  followed  in  the  text-book;  the  Biographical, 
requiring  the  pupil  to  state  all  that  has  been  learned  in 
regard  to  particular  individuals;  and  the  Geographical, 
requiring  a  statement  of  all  important  facts  relating  to 
the  history  of  a  locality.  Many  of  the  topics  treated 
by  the  second  and  third  of  these  methods  necessarily  be- 
come cumulative.  For  instance,  the  facts  relating 
directly  to  George  Washington  will  be  gathered  from 
at  least  three  distinct  and  important  periods  in  our  his- 
tory. A  connected  statement  of  the  important  events 
that  have  taken  place  in  Philadelphia,  or  in  the  valleys  of 
the  Hudson  and  of  Lake  Champlain,  or  in  the  State  of 
Virginia,  will  necessarily  cover  a  large  part  of  the  gen- 
eral subject  in  the  higher  grades.  Such  statements 
must,  of  course,  be  brief,  and  will  often  be  a  mere  chro- 
nological table. 

Many  of  these  reviews  and  certain  parts  of  the  regu- 
lar recitations  may  be  made  spirited  general  exercises 
for  the  whole  class  by  the  use  of  the  slate  or  of  paper. 
The  writing  of  the  few  essential  dates,  the  sequence  of 
important  events,  the  names  of  important  individuals, 
etc.,  are  instances.  The  narrative  reviews  will  neces- 
sarily be,  for  the  most  part,  oral. 

It  will  be  observed  that  the  system  of  reviews  above 
suggested  must,  if  faithfully  carried  out,  result  in  a 
thorough  unifying  of  the  general  subject  in  the  mind 
of  the  pupil. 

Suggestions  for    the  Third  Grade. —  The 

essential  points  requiring  careful  study  and  frequent 
review  in  the  history  assigned  to  the  Third  Grade  are 
given  below.  Other  interesting  facts  usually  stated  in 
text-books  should  be  carefully  read,  but  should  receive 
a  less  proportionate  share  of  attention.  In  no  other 
grade  is  a  frequent  reference  to  the  maps  so  important. 


HISTORY.  193 

SYLLABUS  OF  TOPICS. 

The  voyage  of  Columbus ;  the  naming  of  America ;  the  occu- 
pation of  the  West  India  Islands  and  all  the  neighboring  por- 
tions of  the  continent  by  the  Spaniards ;  their  enslavement  of 
the  Indians  and  its  results  (the  last  very  briefly). 

The  discovery,  exploration,  and  occupation  of  the  St.  Lawrence 
and  Nova  Scotia  by  the  French. 

Virginia. — The  settlement  of  Jamestown  and  the  events 
directly  leading  to  it.  The  cultivation  of  tobacco;  the  intro- 
duction of  slavery  ;  the  navigation  acts  and  Bacon's  rebellion. 

Maryland. — TheCalverts;  religious  freedom;  Clayborne. 

New  England. — The  Plymouth  Company  and  the.  settlements 
under  their  patent.  The  Puritans ;  their  previous  history  and 
why  called  Pilgrims.  The  settlement  of/ Plymouth;  of  Boston; 
of  Dover;  the  Massachusetts  Bay  Colony.  The  settlement  of 
Connecticut;  of  Rhode  Island;  provisions  for  religious  freedom. 
The  Union;  Indian  Wars  (read  only,  and  do  not  commit  the 
details  to  memory).  Andros ;  King  William's  War,  its  causes 
and  results.  The  Salem  Witchcraft  (read).  Queen  Anne's  War, 
its  causes  and  results.  King  George's  War,  its  causes  and 
results. 

New  Netlierlands. — Henry  Hudson  ;  the  settlement  on  the  Del- 
aware ;  at  Fort  Orange;  at  Manhattan  Island;  the  Dutch  Gov- 
ernors ;  Kieft's  conduct :  Stuyvesant. 

New  York. — Changes  of  name;  reconquest  by  the  Dutch  and 
final  restoration  to  England.  Andros ;  the  extent  of  his  rule. 
Dongan;  Leisler;  the  burning  of  Schenectady ;  the  Negro  plot. 

New  Jersey. — Its  name  ;  its  division ;  union  with  New  York  ; 
final  separation. 

Delaware. — Its  settlement  by  Swedes;  its  conquest  by  Stuy- 
vesunt. 

Pennsylvania. — William  Penn  ;  his  grant ;  his  objects.  The 
settlement  of  Philadelphia;  the  relations  of  Pennsylvania  to 
Delaware. 

North  Carolina.— The  grant  of  Charles  II.  ;  its  geographical 
limits ;  John  Locke. 

South  Carolina.— Charleston  settled;  Carolina  divided  into 
two  separate  governments  in  1729. 

Georgia.— Savannah  settled  ;  character  and  purposes  of  Ogle- 
thorpe. 

9 


194  HOW  TO  TEACH 

The  general  condition  of  the  English  colonies  in  1752.  Their 
population  ;  their  national  derivation  ;  their  industries,  social 
condition,  planters,  patrons,  and  proprietors  ;  the  causes  which 
were  developing  a  love  of  liberty. 

Review  chronologically  under  heads  of  the  following  sovereigns 
of  England  :  Elizabeth  ;  James  I. ;  Charles  I.;  Cromwell ;  Charles 
II.;  James  II.;  William  and  Mary;  Anne ;  George  I.;  George  II.; 
also, Uographically ,  referring  to  Columbus,  De  Soto,  Cortez,  Car- 
tier,  Raleigh,  etc.,  etc. 

The  French  and  Indian  War. — This  should  be  taught  in  out- 
line, the  principal  points  being  :— The  gradual  extension  of  the 
English  and  French  settlements  leading  to  conflicting  claims  ; 
the  explorations  and  posts  of  the  French  in  the  valleys  of  the 
Mississippi,  the.  St.  Lawrence,  and  the  Lakes ;  Marquette  and 
La  Salle  ;  the  debatable  laud  on  the  upper  Ohio ;  relatively 
small  population  of  Canada  ;  the  building  of  Fort  Du  Quesne, 
1754 ;  Colonial  Congress  at  Albany,  1754 ;  Braddock's  and 
Johnson's  Expeditious,  and  their  results,  1755 ;  Monckton's 
Expedition  in  1755  ;  cruel  expulsion  of  the  Acadiaus ;  capture  of 
Oswego,  1756 ;  Fort  William  Henry,  1757 ;  siege  and  capture  of 
Louisburg,  1758 ;  repulse  at  Ticonderoga,  1758;  concentration 
of  French  forces  at  Quebec,  by  abandoning  nearly  all  other 
posts ;  battle  of  Quebec,  1759  ;  results  ;  Treaty  of  Paris,  1763  ;  its 
conditions. 

In  teaching  the  French  and  Indian  War  let  the  ten  dates 
marked  be  studied  by  the  years  only.  Read,  but  do  not  memor- 
ize, the  details  of  military  movements  and  events  ;  fix  the  se- 
quence of  events ;  use  the  map. 

In  the  biographical  review,  let  the  pupil  tell  very  briefly  of 
Washington,  Braddock,  Johnson,  Monckton,  Amherst,  Aber- 
crombie,  Howe,  Wolfe,  Dieskau,  and  Montcalm. 

ELEMENTARY  SCIENCE. 

(For  Oral  Instruction.) 

PHYSIOLOGY   AND   HYGIENE. 

The  chief  purpose  of  this  study  as  a  branch  of  Com- 
mon School  instruction  is,  to  give  useful  practical 
knowledge  of  the  laws  of  health.  As  the  subject  can 


ELEMENTARY  SCIENCE.  105 

receive,  at  most,  but  a  small  part  of  the  time  assigned  to 
a  single  grade,  it  is  the  more  important  that  only  those 
parts  of  the  study  should  be  considered  that  are  essen- 
tial to  the  main  purpose.  Anatomy,  which  occupies  so 
much  space  in  many  text-books,  should  not  take  up  the 
time  of  the  pupil,  excepting  so  far  as  it  may  be  absolutely 
necessary  in  order  to  teach  the  physiology  and  hy- 
giene. It  is  a  matter  of  little  consequence  to  the  pupil 
to  know  exactly  the  number  of  bones,  or  of  pairs  of  mus- 
cles in  his  body,  or  to  repeat  their  scientific  names. 
Only  those  terms  and  facts  should  be  introduced  that 
are  actually  necessary  in  order  to  deal  intelligently 
with  the  main  subject.  Oral  description  of  structure 
or  function  should  take  the  place  of  definitions. 

The  appliances  necessary  for  teaching  this  branch  are, 
the  blackboard  and  charts.  The  teacher  should  care- 
fully consider,  at  every  step,  to  what  extent  the  subject 
can  be  treated  objectively.  This  can,  in  part,  be  done  by 
drawing  the  pupil's  attention  to  his  own  body,  as  in 
the  case  of  the  pulse,  the  veins,  arteries,  respiration,  etc. 
For  several  very  important  parts  of  the  subject,  there  is 
no  better  apparatus  than  that  which  can  be  procured 
without  expense  at  any  butcher's  stall,  such  as  the  lungs 
and  windpipe  of  a  sheep ;  the  diaphragm,  the  heart  and 
part  of  the  great  tubes  leading  to  and  from  it ;  the  brain 
and  the  bony  cavity  which  contains  it;  the  eye;  por- 
tions of  the  spinal  cord  and  nerves  ;  small  glands  ;  and 
portions  of  limbs,  showing  the  relations  of  muscles,  ten- 
dons, ligaments,  and  joints.  None  of  these  need  present 
anything  offensive  or  disgusting.  Add  to  these  a  small 
knife,  and  reasonable  preparation  on  the  part  of  the 
teacher,  and  the  instruction  given  will  be  both  interest- 
ing and  profitable.  Where  it  would  not  be  expedient  to 
resort  to  this  means  of  illustration,  preparations  (simi- 


196  HOW  TO  TEACH 

lar  to  those  manufactured  by  Auzout)  could  be  used,  if 
procurable,  and  in  their  absence,  diagrams  and  charts. 
A  syllabus  of  leading  points  is  subjoined.  It  should 
not  be  expected  that  all  these  can  be  taught  in  one 
class,  though  all  are  important,  nor  that  any  point 
should  be  treated  exhaustively. 

SYLLABUS  OF  TOPICS. 

The  pupil  should  be  led  to  look  upon  the  body  as  a  complex 
apparatus  for  the  use  of  his  mind.  To  know  that  it  consists  pri- 
marily of— 

First,  a  bony  frame-work  (the  skeleton) ;  second,  a  motor  ap- 
paratus attached  to  the  frame  (the  muscular  system) ;  third,  a 
directing  apparatus  by  which  the  mind  controls  the  body  (the 
brain,  the  nervous  system,  and  the  sensory  organs) ;  fourth,  a 
general  envelope  protecting  all  the  preceding,  as  well  as  serving 
other  purposes  (the  skin). 

He  should  then  be  led  to  see  that  every  motion  of  the  body  or 
of  its  minutest  part,  however  slight,  and  whether  voluntary  or  in- 
voluntary, requires  the  destruction  of  a  minute  part  of  the  organ- 
ism and  the  removal  of  the  destroyed  part  from  the  system  ; 
that  this  constant  destruction  and  removal  make  necessary  a  cor- 
responding reconstruction  and  renewal,  by  means  of  new  mate- 
rial;  and  that  for  these  purposes  there  are  provided,  fifth,  a  cir- 
culatory apparatus  (the  blood  vessels),  to  carry  away  old  material 
and  to  distribute  the  new  ;  sixth,  an  aerating  apparatus  (the  res- 
piratory system),  to  purify,  warm,  and  enliven  the  circulating 
fluid  ;  seventh,  a  system  of  drainage  (the  skin  and  the  kidneys), 
to  take  from  the  blood  a  large  part  of  the  worn-out  material ; 
and  eighth,  an  apparatus  to  prepare  and  supply  the  new  ma- 
terial (the  digestive  and  assimilative  organs). 

Under  each  of  these  heads  a  few  points  are  noted  : 

1.  The  bones, — their  composition  and  various  uses  :  joints  and 
their  lubrication  ;  important  peculiarities  of  the  spinal  column  ; 
cautions  as  to  injuring  the  large  bones  of  an  infant ;  the  repair 
of  broken  bones,  how  effected. 

2.  The  muscles  and  tendons, — their  uses  ;  their  arrangement  in 


ELEMENT  A  R  Y  SCIENCE.  197 

pairs,  and  why;  how  attached;  how  able  to  contract;  effects  of 
exercise  ;  use  of  calisthenics. 

3.  The  nervous  system, — the  means  of  becoming  conscious  of  the 
external  world;  the  spinal  cord;  its  importance  and  protection; 
its  ramifications;  effects  of  severing  or  injuring  the  spinal  cord; 
care  of  infants  in  this  respect.     The  sympathetic  system ;  the 
nerves  as  telegraph  wires;  the  brain  and  its  principal  functions; 
uses  of  sleep ;  late  hours,  stimulants,  elc. 

The  organs  of  the  special  senses, — touch,  papillae  ;  taste  ;  smell; 
the  ear,  its  mechanism,  hearing  ;  the  eye,  its  mechanism,  sight ; 
abuse  of  the  eyes  ;  myopy,  its  causes  and  prevention. 

4.  The  skin, — its  structure  and  uses  ;  the  perspiratory  glands 
and  tubes  ;  uses  of  perspiration  ;    importance    of  bathing ;  the 
proper  time  for  bathing ;  proper  clothing  ;  sympathy  of  the  skin 
with  the  lungs,  with  the  digestive  organs ;  caution  against  the 
exposure  of  the  limbs,  arms,  or  chests  of  little  children  ;  the  skin 
as  an  absorbent ;  danger  of  cosmetics  and  hair-dyes  ;  treatment 
of  burns  and  scalds,  etc. 

5.  The  circulatory  system, — the  general  relations  of  the  heart, 
arteries,  veins,  and  capillaries ;  the  valves  ;  the  pulse  ;  its  rate  ;  the 
rapidity  of  circulation.   Effects  of  fresh  air  and  exercise  on  the  cir- 
culation ;  limits  of  exercise  ;  dangers  of  excessive  rope-jumping, 
etc.     Effects  of  sleep  on  the  circulation ;  effects  of  tight  gar- 
ments ;  of  insufficient  or  improper  food ;  wounds  ;  how  to  know 
when  an  artery  is  wounded,  and  what  to  do. 

6.  The  respiratory  system.— (Practically  the  most  important  part 
of  hygienic  knowledge).      The  apparatus;  how  protected;  ar- 
rangement of  the  ribs  for  flexibility,  and  for  the  expansion  of  the 
lungs  ;  the  muscles  of  the  chest  and  the  diaphragm ;  importance 
of  the  diaphragm ;  (show  its  positions  at  the  beginning  and  at 
the  end  of   an   inspiration  ;)   the   trachea  ;   the  vocal  chords ; 
structure  of  the  lungs  ;  its  air  cells,  and  their  membrane  ;  exos- 
mosis  and  endosmosis  as  concerned  in  respiration  ;  intimate  re- 
lations of  the  capillaries  and  air  vessels  ;  frequent  full  inspira- 
tions a  means  of  increasing  the  capacity  of  the  lungs  ;  perni- 
cious effects  of  tight  lacing  on  the  capacity  and  action  of  the 
lungs.     The  air, — its  composition  ;  relations  of  oxygen   to  the 
carbon  and  the  hydrogen  introduced  with  the  food  ;  products  of 
respiration  all  invisible  excepting  watery  vapor  ;  the  poisonous 
nature  of  carbonic  acid  ;  danger  from  it  in  wells,  and  in  vats : 


198  HOW  TO  TEACH. 

the  effects  of  smaller  quantities;  the  other  substances  thrown  off 
by  the  lungs  and  the  skin ;  the  ventilation  of  class-rooms 
and  of  sleeping-rooms ;  effects  of  foul  air  from  cellars,  sewers, 
sinks,  water-pipes,  garbage,  gas-lights, "  stoves,  etc. ;  simple  and 
cheap  disinfectants;  chloride  of  lime;  chlorine;  sulphate  of 
iron  ;  carbolic  acid,  etc.  Respiration  as  affected  by  position,  in 
standing,  or  in  sitting,  and  especially  in  sitting  to  write  or  to 
draw. 

7.  The  digestive  apparatus, — the  teeth,  their  uses,  structure,  and 
hygiene  ;  a  brief  notice  of  the  salivary  glands,  their  position  and 
uses  ;  of  the  gullet ;  of  the  structure  and  function  of  the  stomach ; 
a  brief  notice  of  the  duodenum,  the  intestines,  and  the  lacteals  ; 
the  importance  and  functions  of  the  liver  ;  the  thoracic  duct  as 
the  link  between  the  digestive  and  the  circulatory  systems.  Dys- 
pepsia, its  preventable  causes  and  terrible  consequences  ;  common 
errors  to  be  avoided  in  the  preparation  of  food  ;  common  poisons 
and  their  antidotes. 


SECOND    GKADE 

OUTLINE    COUESE. 
Time  allowed,  about  ten  monflis. 


LANGUAGE. 

Reading. — Of  the  grade  of  a  Fifth  Reader,  with  instruction 
and  exercises  in  elocutionary  principles,  and  in  vocal  culture,  aa 
in  the  preceding  grade. 

Spelling. — Continued  as  in  the  preceding  grade. 

Definitions. — As  in  the  preceding  grade,  with  word  analysis, 
or  etymology. 

English  Grammar. — Analysis,  parsing,  and  construction 
continued  ;  also  the  correction  of  false  syntax. 

Composition. — Continued. 

ARITHMETIC. 

Menta*  and  Written. — Commercial  rules,  through  per- 
centage, including  profit  and  loss,  commission,  insurance,  stocks, 
interest,  discount,  etc. ;  with  carefully  graded  exercises  in  analy- 
sis and  calculation. 

The  problems,  to  teach  and  illustrate  the  methods  of  compu- 
tation employed  in  ordinary  business  transactions. 

GEOGRAPHY  AND  HISTORY. 

Geography. — Of  Asia,  Africa,  and  Oceanica,  both  local  and 
descriptive ;  an  outline  review  of  the  topics  of  .he  preceding 
grades. 


200  IIOW  TO  TEACH 


History. — Of  the  United  States,  from  1763  to  the  present 
time,  including  the  outlines  of  the  Revolutionary  War,  the  forma- 
tion of  the  Union,  the  chief  events  of  the  national  history,  includ- 
ing also  a  brief  outline  of  the  great  Civil  War  of  1861-5,  and  its 
results. 


ELEMENTARY  SCIENCE. 

BY   ORAL.   INSTRUCTION   OR   WITH   A   SIMPLE    TEXT-BOOK. 

Natural  Philosophy. — The  outlines  of  mechanics,  hydro- 
statics, and  pneumatics. 

Astronomy. — Elementary  astronomy,  to  include  an  explana- 
tion of  the  ordinary  phenomena,  and  a  brief  account  of  the  bodies 
constituting  the  Solar  System. 

WRITING  AND  DRAWING. 

Penmanship, — Instruction  and  exercises  of  a  similar  char- 
acter to  those  of  the  preceding  grade,  but  more  advanced. 

Drawing.— Cor,  tinned  practice  in  the  work  prescribed  for  the 
preceding  grades,  to  which  should  be  added  the  sphere,  the  ob- 
late and  oblong  spheroids,  the  hemisphere,  with  first  lessons  in 
shading  ;  also  the  drawing  of  rectangular  solids  from  blocks  in 
various  positions,  with  a  few  simple  directions  as  to  perspective. 
Drawing  from  objects,  natural  fruit  and  plant  forms,  also  con. 
Ventional  forms,  and  the  composition  of  designs. 


READING. 


SUBJECTS     OP    THK    SECOND    GRADE 


LANGUAGE. 

Reading. — In  this  grade,  the  simple  principles  of 
elocution,  taught  in  the  preceding  grades,  should  be 
carefully  reviewed,  and  exercises  to  cultivate  the  voice, 
and  confirm  habits  of  distinct  articulation  should  be 
continued  to  some  extent.  The  rationale  of  good  read- 
ing should,  as  occasion  offers,  be  more  fully  explained, 
particularly  as  regards  emphasis  and  modulation.  Emo- 
tional reading  should  receive  a  fair  share  of  attention. 
In  classes  or  schools  for  males,  exercises  in  declamation 
and  recitation  will  be  useful  as  an  auxiliary. 

The  pieces  read,  being  of  a  higher  order  of  style  and 
subject,  should  receive  a  more  careful  analysis  on  the 
part  of  the  teacher,  so  as,  by  interrogation,  to  lead  the 
minds  of  the  pupils  to  a  proper  understanding  of  their 
subject-matter,  and  enable  them  to  obtain  all  the  infor- 
mation and  culture  of  mind  which  they  may  be  made 
the  vehicle  of  imparting.  Much  time  is  apt  to  be  mis- 
spent in  this  grade  by  simply  permitting  the  pupils 
to  read  mechanically  and  listlessly  pieces  of  difficult 
prose  and  poetry,  which  by  earnest  teaching  might  be 
made  to  fix  in  the  minds,  and  often  in  the  hearts,  of  the 
pupils  so  much  that  is  valuable.  Few  tests  of  the  ear- 
nestness and  skill  of  a  teacher  are  so  thorough  as  the 
teaching  of  reading  in  this  grade  and  the  next.  The 


202  H.OW  TO  TEACH 

subject,  the  style,  the  difficult  or  unusual  words,  the  al- 
lusions, the  course  of  reasoning,  mode  of  treatment, 
etc.,  may  all  be  made  the  basis  of  useful  investigation 
by  the  pupil  or  of  comment  by  the  teacher. 

The  pieces  read  should  comprehend  a  sufficient  vari- 
ety, both  as  to  style  and  subject,  to  afford  scope  for  what 
is  above  suggested.  They  should  include  didactic,  narra- 
tive, argumentative  and  oratorical  selections;  extracts 
from  distinguished  writers  in  history,  biography,  popular 
science,  etc.,  as  well  as  the  various  departments  of  poe- 
try ;  an  important  object  of  the  instruction  being  to  give 
a  taste  for  reading  more  fully  the  works  or  compositions 
from  which  the  extracts  are  made.  Some  account  of  the 
authors  should  be  given  in  connection  with  the  lessons. 

Definitions  and  Word  Analysis. — The  prc- 
fixes  and  suffixes  learned  in  the  preceding  grades  should 
be  reviewed  by  means  of  appropriate  exercises  involv- 
ing the  application  of  easy  roots.  For  this  purpose  such 
words  as  the  following  may  be  used  -  —  Drunkard, 
Thralldow,  Depth,  ^4&duct,  Version,  'Local, — involving 
English,  or  Anglo-Saxon,  and  Latin  affixes  only. 

Next,  the  exercises  should  involve  the  use  of  easy 
Latin  roots,  such  words  as  the  following  being  used : 
Avert,  A&vert,  Convert,  Pervert,  etc. — verse,  version, 
diverse,  etc.  The  application  of  various  affixes,  so  as  to 
form  several  words  from  the  same  root,  will  serve  to  im- 
press the  meaning  of  the  root,  in  its  various  forms,  on 
the  mind  of  the  pupil,  as  well  as  to  review  the  affixes. 
Latin  words  need  not  be  taught. 

After  a  few  exercises  of  this  kind,  words  containing 
miscellaneous  roots  may  be  used;  as,  Predict,  Submit, 
"Reject,  Invade,  etc. ;  then  words  containing  prefixes  and 
suffixes,  as,  Subwmsion,  Objection,  Confluent,  Procedure, 


DEFINITIONS  AND  WORD  ANALYSIS.          203 

etc. ;  care  being  taken  at  first  to  select  such  words  as 
are  regularly  formed,  and  the  literal  signification  of 
which  exactly  or  nearly  agrees  with  the  actual  meaning 
as  used. 

The  following  form  of  analysis  is  suggested:  Abduct, 
— formed  from  the  root  duct  which  means  to  lead,  and 
the  prefix  ab,  which  means  away.  Hence,  abduct 
means  to  lead  aivay.  Actual  meaning,  to  take  away  by 
stealth  ;  as,  "  They  tried  to  abduct  the  child  from  his 
parents." 

In  this  form  of  analysis,  the  root  and  its  meaning  are 
first  stated;  next,  the  suffix;  then,  the  prefix,  and  then 
the  literal  meaning  of  the  word,  to  be  followed  in  all 
cases  by  the  actual  meaning,  which  is  to  be  exemplified 
in  a  sentence. 

After  the  pupil  is  sufficiently  initiated  in  the  method 
so  as  to  analyze  words  with  some  degree  of  facility,  the 
principal  Latin  roots  should  be  taken  up  and  taught 
exhaustively,  alphabetically,  or  in  the  order  of  their 
difficulty.  These  should  be  followed  by  a  few  of  the 
Greek  roots,  suffixes  and  prefixes,  to  be  followed  by  the 
French  or  other  foreign  roots.  The  Anglo-Saxon  or 
English  roots  should,  if  taught  at  all,  follow  these. 
All  beyond  the  Latin  roots,  and  if  necessary  some  of 
these,  may  be  reserved  for  the  First  Grade. 

Exercises  in  information  of  words  from  given  roots 
should  form  a  prominent  part  of  the  exercises  used  to 
familiarize  the  pupils  with  the  meaning  of  the  roots, 
well  as  the  meaning  of  words  derived  from  them.  For 
the  purpose  of  this  instruction  the  English  form  of  the 
root  is  all  that  needs  to  be  taught.  In  this  way  the 
subject  will  be  freed  from  much  complexity.  Thus, 
after  analyzing  the  Avord  dentist,  the  pupil  gives,  as  far 
as  he  can  recall  to  mind,  the  words  derived  from  the 


204  HOW  TO  TEACH 

root  dent ;  as  dental,  dent-die,  dentoid.,  dentition,  denti- 
frice,  dentiform,  indent,  etc.  Words  such  as  dentistry 
are  to  be  considered  as  of  secondary  formation,  and  to 
be  analyzed  by  considering  dentist  the  primitive.  In 
this  way  the  analysis  of  a  very  large  class  of  words  will 
be  greatly  simplified. 

The  analysis  of  words  is,  of  course,  etymological ;  but 
it  is  rather  introductory  to  the  study  of  etymology 
than,  properly  considered,  a  part  of  that  study.  The 
science  which  treats  more  directly  and  specially  of  the 
origin  and  relation  of  verbal  forms,  their  primitive 
meaning,  their  combinations,  and  the  varied  significa- 
tions with  which  their  derivatives  have  been  used  from 
time  to  time,  is  scarcely  appropriate  at  this  stage  of  the 
pupil's  progress.  The  instruction  derived  from  such 
exercises  as  are  above  indicated  is  exceedingly  valuable 
for  its  practical  usefulness;  but  such  facts  as  that  half 
is  the  Anglo-Saxon  healf,  home  the  Anglo-Saxon  hdm, 
and  the  German  Jieim,  etc.,  etc.,  are  interesting  and 
useful  for  a  very  different  purpose,  and  should  occupy 
a  more  advanced  place  in  an  educational  scheme. 

English  Grammar. — In  this  grade,  the  pupils 
should  be  exercised  in  the  analysis  and  parsing  of  sen- 
tences of  a  higher  grade  of  difficulty  ;  but  those  of  anom- 
alous or  peculiar  construction  should  be  avoided.  The 
analysis,  except  for  review,  should  be  only  in  outline, 
so  as  to  show  the  "general  structure  of  the  sentence," 
and  enable  the  pupil  to  see  clearly  the  relation  of  the 
clauses  or  members.  This  is  essential  to  a  correct  and 
definite  understanding  of  the  meaning  of  the  sentence, 
as  well  as  for  the  application  of  rules  having  reference 
to  the  construction  of  sentences.  Some  knowledge  of 
punctuation  should  be  imparted  in  this  connection. 


GRAMMAR.  205 

The  following  sentence  analyzed  will  illustrate  the 
requirements  of  this  grade  in  this  respect: 

"Pay  the  debts  which  thou  owest ;  for  he  who  gave 
thee  credit  relied  upon  thy  honor,  and  to  ivithhold  from 
him  his  due  is  both  mean  and  unjust" 

Analysis. — This  sentence  consists  of  two  members: 
1.  "  Pay  the  debts,"  etc.,  to  "  owest ;  "  2.  "  He  who  gave 
thee,"  etc.,  to  "  unjust."  These  members  are  connected 
by  "for." 

The  first  member  contains  the  clause  "which  thou 
owest"  used  as  an  adjunct  of  " debts." 

The  second  member  consists  of  the  two  clauses :  "He 
who  gave  thee,"  etc.,  to  "honor,"  and  "To  ivithhold" 
etc.,  to  "  unjust." 

This  should  be  followed  by  the  parsing  of  the  most 
important  words,  which  will  show  whether  a  more  mi- 
nute analysis  of  the  sentence  should  be  required  of  the 
pupil  or  not. 

As  far  as  may  be  necessary,  the  structure  of  the  sen- 
tence, discovered  by  analysis,  should  be  made  the  subject 
of  rhetorical  criticism,  with  reference  to  its  clearness  in 
expressing  the  meaning  intended  to  be  conveyed,  its^?*0- 
priety,  unity,  harmony,  etc.  The  thought  itself  may  be, 
to  some  extent,  analyzed,  and  subjected  to  critical  remark. 

The  parsing,  as  an  application  of  the  rules  and  prin- 
ciples peculiar  to  our  own  language,  should  also,  as 
far  as  possible,  be  so  conducted  as  to  have  a  critical  end 
in  view.  This  will  greatly  improve  the  pupils  in  their 
use  of  language,  by  rendering  them  more  alert  in  dis- 
covering inaccuracies,  as  well  as  by  impressing  more 
deeply  upon  their  minds  a  knowledge  of  the  rules  by 
which  they  should  be  guided  in  expression. 

Exercises  in  the  correction  of  false  syntax  should  be 
abundantly  used  in  this  grade. 


206  SOW  TO  TEACH 

Composition. — The  construction  of  sentences 
should  assume  the  character  of  extended  composition, 
the  themes  being  selected  by  the  pupils  themselves  or 
assigned  by  the  teacher.  Of  course,  care  should  be 
taken  that  the  themes  are  of  a  simple  character — ap- 
propriate to  the  mind  of  a  child,  and  calculated  to 
awaken  thought,  not  to  repress  it,  as  is  too  often  the 
case  when  difficult  subjects,  of  an  abstract  or  too 
comprehensive  character,  are  chosen  for  the  exercise. 

ARITHMETIC. 

The  commercial  arithmetic  of  this  grade  differs  from 
that  taught  in  the  preceding  grades,  chiefly  in  the  in- 
troduction of  the  various  forms  of  percentage.  The 
divisions  of  percentage  should  be  presented  in  the  fol- 
lowing order :  First,  simple  percentage,  in  four  cases — 
one  fundamental  and  three  derived;  second,  the  appli- 
cations of  simple  percentage,  technically  known  as  Com- 
mission, Brokerage,  and  Profit  and  Loss,  following  the 
same  order  and  with  the  same  analysis  as  in  the  four 
cases  of  simple  percentage. 

Those  who  prefer  to  do  so  may  readily  combine  these 
divisions  under  the  general  head  of  "percentage  not  in- 
volving time." 

The  third  division  of  the  subject  is  interest,  or  "  per- 
centage  involving  time."  It  has  five  cases — one  funda- 
mental and  four  derived. 

In  treating  the  percentage  rules  many  skillful  teach- 
ers prefer  to  introduce  algebraic  formulae,  in  which  the 
initial  letters  of  the  several  terms  employed  in  percen- 
tage are  the  elements.  To  this  course  there  is  no  ob- 
jection, provided  that  the  formulas  be  not  employed  in 
the  mental  arithmetic,  and  that  they  accompany  the 


ARITHMETIC.  207 

usual  analysis  and  be  not  used  us  a  substitute  for  it. 
With  this  exception,  the  processes  and  explanations  of 
the  mental  arithmetic  should  not  differ  from  those  of 
the  written  arithmetic,  the  chief  distinction  between 
the  two  being,  that  in  the  latter  the  numbers  are  too 
large  to  be  carried  in  the  mind. 

The  subject  of  arithmetic  being  necessarily  to  a 
great  extent  cumulative,  the  teacher  of  this  grade  is 
especially  advised  to  read  over  the  directions  given  in  the 
preceding  grades,  and  in  particular  the  table  on  page 
162.  For  the  sake  of  brevity,  the  terms  base,  percent- 
age, etc.,  are  employed  in  the  following  syllabus  of  top- 
ics in  the  usual  technical  sense  of  the  text-books. 

SYLLABUS  OP  TOPICS. 

The  term  percentage — exercises  in  reading  per  cent. 

Examples — Read  the  following,  exemplified  and  defined  first 
as  decimal  fractious,  and  then  as  per  cent. :  .75,  .8,  .605,  .003, 
.08i,  .OOi,  etc. 

Exercises  5u  changing  common  fractions  to  per  cent.  and. 
vice  versa : 

Examples— |,  \,  fftg,  |i,  2£,  I,2-,,  |f,  etc.,  how  many  hun- 
dredths  ?  what  per  cent.  ? 

Examples— 25  per  cent.,  75  per  cent,  33^  per  cent.,  14?  per 
cent.,  88|  per  cent.,  325  per  cent.,  137^  per  cent.,  etc.,  are  equiv- 
alent to  what  common  fractions? 

NOTE.— The  common  business  fractions,  halves,  thirds,  etc.,  to  twelfths, 
inclusive,  should  be  reduced  to  per  cent.,  and  the  pupils  made  thoroughly 
familiar  with  them. 

SIMPLE   PERCENTAGE. 

IST  CASE  (Fundamental).— -To  find  the  percentage,  the  base  and 
rate  being  given. 

See  table,  page  102.— To  find  a  given  fractional  part  of  a 
given  number. 


208  HOW  TO  TEACH 

Examples— How  much  is  9  per  cent,  of  750  ?    Had  $750  in 
the  bank;  drew  out  9  per  cent.     How  much  was  it? 
Analysis  as  in  the  multiplication  of  decimal  fractious. 

NOTE.— When  this  form  of  the  case   has  been  taught,  it*  modifications 
should  immediately  follow. 

Example — Had  $750;  paid  out  9  per  cent.     How  much  had 
Heft? 

Example — Had  $750 ;  earned  9  per  cent.  more.     How  much 
had  I  then  ? 

2o  CASE  (Derived). — To  find  the  rate  when  the  percentage  and 
base  are  given. 

See  table,  page  162. — Tofind  what  fraction  one  given  number 
is  of  another  given  number. 

Examples — 140  is  what  per  cent,  of  400  ? 

"  Had  400  sheep ;  sold  140.    What  per  cent,  did  I 

sell? 

Analysis  as  in  reducing  a  common  fraction  to  a  decimal  frac- 
tion whose  denominator  is  hundredths. 

Modifications  of  Case  3d  : 

Example — I  had  400  sheep;  I  now  have  540.     What  is  the 
per  cent,  of  increase  ? 

Example — I  had  400  sheep ;  I  now  have  only  260.     What  is 
the  per  cent,  of  decrease?  or,  what  per  cent,  have  I  left? 

3d.  CASE  (Derived). — To  find  the  base  when  the  percentage  and 
the  rate  are  given. 

See  table,  page  162. — To  find  the  number  of  which  another 
number  is  a  given  fraction. 

Example — 140  is  35  per  cent,  of  what  number  ? 

Sold  140  sheep,  which  was  35  per  cent,  of  my  flock. 
How  many  had  I  at  first  ? 

Analysis  as  in  simple  fractions — 140  is  /.A,  of  what  number? 

Modifications  of  Case  3d  : 

Example — Sold    140  sheep,  which  was  35  per  cent,   of  my 
flock.     How  many  had  I  left? 

Example — Sold  140  sheep,  and  have  65  per  cent,  of  my  flock 
remaining.     How  many  had  I  at  first  ? 

4th  CASE  (Derived.) — To  find  the  base  when  the  amount  (or 
difference)  and  rate  are  given. 

To  find  a  number  which  differs  by  a  given  fractional  part  of 
itself  from  a  'riven  number. 


ARITHMETIC.  209 

Example— What  number  is  by  8  per  cent,  of  itself  more  than 
351  ?  or  351  is  8  per  cent,  more  than  what  number  ? 

Example — My  flock  of  sheep  increased  8  per  cent.;  I  then  had 
351.  How  many  had  I  at  first  ? 

Example — I  lost  8  per  cent,  of  my  sheep,  and  had  299  remain- 
ing. How  many  had  I  at  first  V 

NOTE.— Axiom.— The  base  is  100  per  cent,  of  itself.    This  is  only  a  form  of 

the  fundamental  axiom  of  fractions,  1—  — 

n 

f  First,  find  the   per  cent,  of  the  base,  represented 
I      by  the  given  number  ;  100  per  cent. +  8  per  cent. 

of  hi'st  t  wo  -I      =1°8  per  Cent-  of  the  base  :  10°  per  cent-— 8  Per 
examples,     f      cent.  =92  per  cent,  of  the  base. 

Second,  proceed  as  in  3d  case — 351  is  \%l  of  what 
number  ? — 290  is  ^  of  \vhatnumber  ? 

As  a  part  of  the  general  review,  give  an  example  in  the  fun- 
damental case,  and  let  the  pupils  derive  the  other  three  cases 
from  it,  and  then  their  modifications. 

Commission  and  Brokerage  and  Profit  and  Loss  are  b;it  appli- 
cations of  simple  percentage.  Each  presents  itself  under  all 
the  four  cases, but  requires  no  special  additional  teaching,  except 
in  regard  to  the  technical  terms  employed. 

INTEREST. — Teach  the  definitions  of  the  terms  employed  ;  the 
distinction  of  simple  from  compound  interest;  the  legal  rate  of 
U.  S.  and  of  the  State  in  which  the  school  is  situated. 

NOTE. — In  classes  of  an  average  character,  one  good  method,  in  solving  ex- 
amples in  interest,  will  be  found  to  give  better  results  than  two  or  more.. 
Whatever  method  be  employed,  the  pupils  should,  from  the  first,  be  carefully 
guarded  against  considering -and  calling  the  multiplier  a  concrete  number. 
For  instance,  multiplying  $15,  the  interest  for  1  year,  by  3  years,  etc.,  is,  of 
course,  an  absurd  statement. 

If  the  six  per  cent,  method  be  employed,  it  should  be  carefully 
analyzed,  and  the  pupils  should  not  be  allowed  to  sacrifice 
sense  to  conciseness  by  such  statements  as  "  the  half  of  7  months 
is  3  cents-and-a-half " — one-sixth  of  24  clays  is  3  mills,  etc.,  etc. 
As  a  preliminary  to  applying  this  method,  the  class  should  have 
a  thorough  training  on  such  questions  as  the  following  :  Find 
.207  of  $185.75  ;  find  .OG85  of  $36.25  ;  (see  preceding  grade).— In 
2  years,  3  months,  and  20  days,  at  6  per  cent,  per  annum,  what 
decimal  fraction  of  tlie  principal  is  equal  to  the  interest  ?  at  7  per 
cent?  at  5?  at  8?  at  7i?etc. 


210  HOW  TO   TEACH 

Give  examples  involving  the  various  forms  of  tlie  difference 
of  dates—  the  application  of  the  six  per  cent,  method  to  a  given 
or  ascertained  number  of  days.  Example  :  Interest  of  $840  from 
Jan.  5th  to  July  ad,  at  6  per  cent.  Examples  involving  the 
method  when  the  year  is  estimated  to  consist  of  365  days,  should 
also  be  given. 

Give  examples  in  Bank  Discount,  and  explain  its  similarity 
to  Compound  Interest  in  being  the  interest  on  the  amount. 

NOTE—  (On  the  derived  ca  es  of  simple  interest.)—  In  teaching  the  four 
derived  cases  of  simple  interest,  begin  with  an  easy  example  in  the  funda- 
mental case,  and  from  that  derive  the  others  in  their  order,  being  particu- 
larly careful  to  teach  that,  being  derived,  they  all  require  division  ;  that,  to 
find  the  rate,  the  given  interest  is  to  be  divided  by  the  interest  of  the  given 
principal  at  1  per  cent.;  to  find  the  time,  by  the  interest  of  the  given  prin- 
cipal for  1  year  ;  to  find  the  principal,  by  the  interest  of  a  principal  of  $1  ; 
and  that,  in  the  fifth  case,  the  given  amount  is  to  be  divided  by  the  amount 


Give  examples  in  True  Discount,  distinguishing  carefully  its 
difference  in  principle,  and  therefore  of  method,  from  Bank  and 
Commercial  Discount 

Partial  Payments  and  Compound  Interest  should  be  very 
briefly  treated,  and  with  very  simple  examples. 

The  form  and  nature  of  a  promissory  note,  and  the  meaning 
of  the  several  terms  applicable  to  it,  and  the  form  of  bills  and 
receipts  are  included  in  the  work  of  this  grade. 


GEOGRAPHY  AND  HISTORY. 


y.  —  Complete  the  local  and  descriptive 
geography  of  one  continent  or  grand  division  before 
beginning  that  of  another.  The  same  general  plan 
should  be  pursued  as  in  the  preceding  grades.  If  the 
prominent  physical  features  of  Asia,  for  instance,  be 
first  taught  as  a  whole,  including  the  climate,  the 
pointer  and  the  outline  map  being  used  to  expedite  the 
process,  the  descriptive  geography  of  the  individual 
countries  will  involve  but  little  labor,  and  will  be 
easily  remembered. 


HISTORY.  211 

The  geography  of  Asia  is  by  far  the  most  important 
and  interesting ;  that  of  Africa  and  Oceanica  is  com- 
paratively simple,  and  should  be  reduced,  in  teaching, 
to  the  narrowest  limits  that  will  give  a  clear  view  of 
the  general  physical  conditions  of  surface  and  climate, 
and  of  the  social  conditions  of  the  various  races,  to- 
gether with  a  knowledge  of  the  leading  productions  and 
exports,  and  the  location  of  the  principal  cities. 

The  whole  subject  of  geography  is  embraced  in  this 
and  the  preceding  grades;  but,  instead  of  a  continuous 
course  as  is  here  indicated,  some  prefer  an  outline  or 
primary  course  at  the  first,  followed  by  an  advanced 
course,  presenting  the  subject  in  full  detail.  This  is 
the  plan  usually  followed  in  geographical  text-books, 
most  series  embracing  a  primary  geography,  and  a 
higher  geography  for  grammar  schools  or  for  the  ad- 
vanced classes  of  district  schools;  and  this  plan  affords, 
especially  in  large  graded  schools,  many  advantages 
over  a  continuous  course. 

History. — The  teacher  is  particularly  referred  to 
the  General  Suggestions  in  regard  to  U.  S.  History,  in 
the  preceding  grade. 

The  Outlines  of  the  Revolutionary/  War. — (Teach  as 
in  the  French  and  Indian  War.) 

Causes  of  the  Revolution. — Navigation  Acts — Restriction  of  Co- 
lonial manufactures — effects  of  war  on  the  national  debt  of  Eng- 
land— taxation  without  representation — the  Stamp  Act,  1765  ;  its 
nature — causes  which  led  to  its  repeal — the  Tea  Tax — riot  in 
Boston,  1770— the  Boston  "  Tea  Party,"  its  immediate  causes, 
and  its  consequences — nature  of  the  Port  Bill,  1774— first  Con- 
gress at  Philadelphia— its  measures— Lexington,  AprilW,  1775— its 
effects  upon  the  country — Bunker  Hill — siege  of  Boston— Wash- 
ington appointed  Commander-in-Chief— evacuation  of  Boston, 


212  HOW  TO  TEACH 

and  subsequent  general  drift  of  military  events  towards  the.  west 
and  south — Declaration  of  Independence,  July  4,  1776 — battle  of 
Long  Island— its  purposes  and  results— retreat  to  the  Delaware 

— capture  of  the  Hessians  at  Trenton — Princeton — La  Fayette 

British  move  on  Philadelphia.  1777— Chad's  Ford— its  conse- 
quences— Burgoyne's  invasion,  its  route  and  purpose,  1777 — 
Schuyler— Burgoyne's  disasters— Gates— the  two  battles  of  Still- 
water — Clinton's  movements— Burgoyne's  surrender,  October, 
1777— its  far-reaching  consequences— the  French  alliance  and 
assistance— British  retreat  from  Philadelphia— Battle  of  Mon- 
mouth,  1778— New  York  the  base  of  the  British— destruction 
along  the  coasts  of  Connecticut  and  Virginia— Wyoming— battle 
of  the  Chemung,  1779— it  breaks  forever  the  power  of  the  Iro- 
quois — Paul  Jones — Charleston  captured,  1780 — large  numbers  of 
Tories  in  the  south — consequent  years  of  guerrilla  warfare — Siur,- 
ter — Marion — Gates  at  Camclen — destruction  of  his  army,  and  of 
Sumter's  force — Arnold's  treason — the  mutiny  at  Morrist.own, 
1781 — its  causes — condition  of  the  army — Robert  Morris — Ar- 
nold's ravages — Greene's  retreat — battles  in  Carolina  and  their 
consequences — Cornwallis  at  Yorktown — combination  of  the 
French  and  American  forces — Surrender  of  Cornwallis,  October, 
1781 — its  effects  in  America  and  in  England — Treaty  of  Paris, 
1783 — its  terms — condition  of  the  country  at  the  close  of  the 
war. 

Articl.-s  of  Confederation,  1776-1777-1781 — the  government 
before  1781 — after  1781 — Shays's  rebellion,  1786 — leads  to  a  con- 
vention to  revise  the  Articles — anew  Constitution  devised  instead, 
1787 — adopted  by  the  States — goes  into  operation,  1789. 

In  the  biographical  review  include  a  brief  notice  of  Henry, 
Hancock,  Franklin,  Lee,  Jay,  Livingston. 

1789-1797. —  Wtuitengton'*  Administration — Domextii  history ; 
the  cabinet — leading  measures — States  admitted — their  former  re- 
lations. Foreign  relations — Trouble  with  France,  and  its  causes. 

NOTE  1 . — Read  the  Indian  war.  The  teacher  will  give  a  brief  statement  con- 
cerning Boone,  Clark,  the  original  extent  of  Virginia,  and  the  Ordinance  of 
1787. 

NOTE  2.—  Give,  orally,  a  very  brief  outline  account  of  the  French  Revolution, 
the  resulting  relations  of  France  and  England  and  of  Europe  generally  ;  the 
rontiiinancc  of  these  wars  to  1815.  Refer  particularly  to  the  fact  that  political 
diffun  nces  in  the  United  States  were,  to  a  great  extent,  based  upon  our  forelgu 


HISTORY.  213 

policy,  and  that  we  were  at  last  drawn  into  the  vortex  of  the  great  European 
wars  in  1812. 

Refer  also  to  Washington's  Farewell  Address,  and  give,  briefly,  a  very  few 
of  its  leading  points. 

1797-1801. — Adams's  Administration.  —  Foreign  relations  ; — 
continued  troubles  with  France. — Domestic  history  ;— unpopular 
measures — the  death  of  Washington— removal  of  the  Capital. 

1801-1809. — Jefferson's  Administration. — Domestic  history  ; — 
admission  of  Ohio — its  previous  relations — the  Louisiana  pur- 
chase— its  immediate  and  subsequent  importance — Hamilton 
and  Burr,  1804 — a  sketch  of  the  history  of  each — Fulton's 
first  steamboat,  1807. — Foreign  relations; — Tripolitan  war,  1801-- 
1805,  its  causes  and  results. — (Read  the  detail.)  The  Btate  of 
Europe,  and  the  importance  of  our  carrying-trade — extraor- 
dinary measures  of  France  and  England  in  relation  to  the 
rights  of  neutrals — English  claims  of  right  of  search  and  im- 
pressment— bearing  of  the  impressment  claim  upon  our  natural- 
ized citizens,  and  our  national  honor — "  Once  a  subject,  always 
a  subject " — affair  of  the  Leopard  and  Chesapeake,  1807 — Or- 
ders in  Council  and  the  Milan  Decree,  1807 — Embargo,  1807- 
1809— Non-intercourse  Act,  1809. 

1809-1817. — Madison's    Administration. — The    entire    interest 
centers  in  the  Foreign  relations— they  control  the  Domestic  history. 
Berlin  Decree  abolished,  1810. 
NOTE.—  Bead  the  affair  of  the  Little  Belt— Indian  War. 

War  declared  June  19,  1812 — its  two  chief  causes. 

NOTE.—  Read  the  detail  ol  the  military  and  naval  operations  ;  show  briefly,  in 
outline,  first,  the  several  aggressive  expeditions  into  Canada,  from  Detroit  to 
the  St.  Lawrence— their  general  failure  ;  second,  the  smallness  of  the  navy— its 
brilliant  success,  but  little  direct  influence  on  the  fortunes  of  the  war,  except- 
ing on  the  lakes— utter  destruction  of  American  commerce  ;  third,  the  aggres- 
sive expedition*  of  the  British,  the  Americans  being  chiefly  on  the  defensive 
after  1812— Indian  war  in  the  West  and  Southwest— invasions  from  Canada- 
blockade  of  all  important  ports— naval  and  military  expedition  against 
Washington  and  Baltimore— invasion  by  the  way  of  Lake  Champlain— expe- 
dition against  New  Orleans,  and  its  purposes— final  repulse  of  all  these  at- 
tempts, and  similar  fate  of  renewed  aggressions  of  the  Americans  against 
Canada— destruction  of  the  Indian  power. 

Give  the  sequence  of  leading  events,  omitting  the  dates,  except  as  to  years. 

The  Hartford  Convention— its  alleged  purposes— its  effects — 
treaty  of  peace,  December,  1814 — a  part  of  the  general  pacifi- 


2U  HOW  TO  TEACH 

cation  of  Europe  upon  the  fall  of  Napoleon — the  causes  of  the 
war  not  even  alluded  to  in  the  treaty — have  these  questions 
ever  been  settled  V  If  so,  when  and  how  ? 

NOTE.— .Sead  the  second  Barbary  war,  1812-1815— its  causes  and  results. 

In  the  biographical  review  include  a  brief  notice  of  Hamilton, 
Burr,  Randolph,  Fulton,  Whitney,  De  Witt  Clinton. 

1817-1825. — Monroe's  Administration. — Domestic  history  ; — Mis- 
souri Compromise,  1820 — formation  of  new  parties  on  questions 
of  commerce  and  finance — Whigs  and  Democrats — the  leading 
questions  until  1845. — Foreign  relations  ; — purchase  of  Florida — 
the  Monroe  Doctrine,  1822,  its  origin  and  importance. 

1825-1829. — John  Quincy  Adamx's  Administration. — Tariff  of 
1828 — leads  to  the  defeat  of  the  Whigs  and  the  election  of  Jack- 
son. 

1829-1837. — Jacfaoris  Administration. — Domestic  history;— 
United  States  Bank — nullification,  1832 — Clay's  Compromise. 
Foreign  relations  ; — the  French  indemnity. 

1837-1841. —  Van  Buren's  Administration.— P&nic  of  1837— Sub- 
Treasury  Bill,  1840— political  revolution. 

1841-1845. — Harrison — Tyler's  Administration. — Domestic  his- 
tory ; — the  Bankrupt  Law — Dorr's  Rebellion. — Foreign,  rela- 
tions ; — the  Maine  boundary — annexation  of  Texas. 

1845-1849. — Folk's  Administration. —  Domestic  relations  now 
give  direction  to  Foreign  policy — Oregon  boundary — chain  of 
causes  leading  to  the  Mexican  war — boundary  claimed  by 
Texas— Mexican  war,  May,  1846,  to  Feb.,  1848. 

NOTE.—  Bead  the  details;  give  the  leading  military  event?  in  sequence, 
omitting  all  dates,  excepting  years.  Teach  with  the  following  grouping. 
Northern  operations— Taylor  east  of  the  Rio  Grande— west  of  it— Wool— Kear- 
ney— Doniphan— Fremont.  Southern  operations — Scott's  campaign. 

Treaty  of  Guadalupe  Hidalgo — its  terms — discovery  of  Cali- 
fornia gold  in  1848 — its  important  subsequent  influence  upon 
the  national  development. 

1850-1853. — Taylor  and  Fillmore's  Administration. — The  Slave- 
ry question  the  leading  element  in  Ihe  subsequent  history — the 
California  question,  1850 — its  alleged  relation  to  the  Missouri 
Compromise — death  of  Taylor — Clay's  Compromise  Bill,  1850. 

1853-1857.—  Pierce's  Administrate .—  Effects  of  the  Fugitive 
Slave  Bill— the  Kansas-Nebraska  Bill,  1854 — it  annuls  the  Mis- 


HISTORY.  215 

souri  Compromise — rise  of  a  new  party,  "  Free-soil "  or  Republi- 
can— civil  war  in  Kansas,  its  causes — flow  of  immigrants  into 
that  territory. 

1857-1861. — Buchanaris  Administration. — Continuation  of  the 
Kansas  trouble— John  Brown's  affair— its  effects—split  of  the 
great  Democratic  party — four  Presidential  candidates — election 
of  Lincoln — extreme  doctrine  of  State  Rights — secession  of 
South  Carolina,  Dec.,  1860 — Fort  Sum ter— more  States  secede — 
Confederate  government  formed,  Feb.,  1861. 

1861-1865. — Lincoln's  Administration. — Civil  war — Fort  Suni- 
ter,  April  12,  1861— effects  upon  the  North— the  President's 
proclamation — more  States  secede,  making  eleven  in  all. 

NOTE.— Head  the  details  of  the  war  ;  show  the  importance  of  the  question 
of  foreign  intervention,  and  the  efforts  on  both  slides  in  regard  to  it. 

In  the  Review  show  that  the  operations  of  the  Confederates  were  mainly 
defensive,  except  in  the  great  sorties  of  Lee  at  Antietam  and  Gettysburg,  of 
Hood  at  Nashville,  and  of  Early  at  Chambersburg— all  of  which  were  repelled. 
That  the  main  objects  of  the  aggressive  movements  of  the  Union  troops  were, 
]st,  the  destruction  of  Lee's  army ;  2d,  The  opening  of  the  Mississippi— that 
after  the  opening  of  that  river  by  the  fall  of  Forts  Henry  and  Donelson,  and 
the  subsequent  capture  of  New  Orleans  and  Vicksburg,  the  lines  were  con- 
tracted by  a  movement  from  the  northwest  to  the  southeast,  ending  in  Sher- 
man's march  from  Atlanta  to  Savannah  and  Goldshoro'.  The  leading  inci- 
dents will  then  readily  fall  into  place.— Show  the  importance  of  the  blockade, 
the  chief  function  of  the  fleet— also,  but  very  briefly,  the  enormous  expendi- 
ture of  men  and  money  on  both  sides,  and  the  measures  by  which  they  were 
obtained. 

1865-1869. — Johnson's  Administration. — Death  of  Lincoln — the 
two  subjects  of  leading  importance — 1st.  Providing  for  the  pub- 
lic debt  —  2d.  Reconstruction  —  the  13th  Amendment  —  the 
President  and  Congress  quarrel — impeachment — the  French 
in  Mexico,  and  the  demand  of  the  United  States  Government — 
purchase  of  Alaska — laying  of  the  first  Atlantic  telegraph 
cable. 

1869-1873.— Grant's  Administration.—  Pacific  Railway— 14th 
and  15th  Amendments — the  Alabama  question — leading  pro- 
visions of  the  treaty  of  Washington — the  Geneva  Arbitration— 
the  settlement  of  the  northwest  boundary  question. 

Addenda — The  rapid  development  of  the  country  since  1815 
— the  leading  elements  in  that  development — emigration  and 
immigration — the  Erie  Canal  and  the  Lakes  as  the  great  water- 


216  BOW  TO   TEACH 

way — steam  and  steamboats — railways — telegmpns.  In  the 
biographical  review  include  a  notice  of  prominent  men,  such 
as  Callioun,  Clay,  Webster,  So  ward,  Greeley,  Morse,  etc.,  etc. 


ELEMENTARY  SCIENCE. 

Natural  Pliilosopliy. — The  suggestion  to  use 
"a  simple  text-book"  should  not  be  interpreted  as  a 
recommendation  to  dispense  with  oral  instruction  in 
this  branch.  On  the  contrary,  the  proper  use  of  the 
text-book  is  as  an  auxiliary,  as  a  general  guide  to  the 
teacher  in  the  selection  of  subjects,  and  as  an  important 
help  to  ihe  pupil  in  preparing  at  home  for  the  recita- 
tion of  a  lesson  Avhich  has  been  previously  explained 
and  illustrated  in  the  class-room. 

Any  system  of  procedure  which  omits  this  prelimi- 
nary oral  instruction  is  certainly  not  worthy  of  the 
name  of  teaching.  The  text-book  should  be  indeed 
brief  and  simple,  and  its  illustrations  must  necessarily 
be  few.  But  the  teacher  should  supply  the  further 
illustration  and  experiment  which  will  certainly  be 
found  to  be  necessary;  it  is  also  of  especial  importance 
that  the  pupils  should  themselves  be  in  every  way  en- 
couraged and  led  to  report  such  instances  of  the  appli- 
cations of  the  principles  they  have  been  taught,  as  they 
can  themselves  discover  in  the  phenomena  and  inci- 
dents of  their  daily  life  and  experience,  both  in  and  out 
of  school,  so  that,  as  far  as  possible,  they  may  form 
habits  of  observation  and  reflection. 

The  teacher  will  find  a  wide  difference  in  the  readi- 
ness with  which  individual  pupils  will  conceive  and 
apply  scientific  principles.  With  a  few,  the  bare  state- 
ment of  a  principle  will  often  enable  them  to  point  out 


ELEMENTARY  SCIENCE.  217 

its  simpler  applications.  The  results  of  a  certain  order 
of  experiments,  and  the  simpler  deductions  from  them, 
will  be  promptly  anticipated  by  such  minds.  But  it 
will  not  be  so  with  all ;  and  with  some,  only  by  careful 
and  repeated  illustration  \vill  the  principles  which  in- 
terpret the  facts  presented,  be  clearly  apprehended.  In 
all  experiments  the  pupils  themselves  should  be  made 
as  far  as  possible  participants.  In  reviews  they  should 
be  called  upon  to  repeat  the  experiments  or  statements 
made  by  the  teacher  or  given  in  the  text,  and  to  give 
the  proper  explanation.  They  should  also  be  encour- 
aged to  try  further  experiments  for  themselves  at  home, 
and  to  furnish  an  account  or  a  repetition  of  them  in 
the  class-room,  if  possible. 

The  teacher  should  also  particularly  remember  that 
it  is  not  necessary  to  follow  slavishly  the  exact  order  01 
selection  of  topics  given  in  the  text-book.  The  teach- 
er, and  not  the  book,  should  be  the  master.  An  intel- 
ligent pupil  will  not  be  long  in  finding  out  whether  or 
not  the  statements  in  the  text  are  the  limit  of  his  teach- 
er's acquisitions.  The  great  majority  of  young  minds 
are  hungry  for  this  sort  of  knowledge,  and  it  will  un- 
questionbly  be  the  teacher's  fault  if  that  appetite  be 
not  at  the  same  time  both  gratified  and  stimulated. 

Care  should  be  taken,  when  the  scientific  meaning 
of  a  common  term  differs  greatly  from  the  popular  one, 
to  point  out  clearly  such  difference,  in  order  that  the 
pupil  be  not  misled  by  thinking  that  he  knows  that  of 
which  he  is  really  ignorant.  Among  the  many  cases 
in  which  this  will  be  found  necessary,  the  terms  poros- 
ity, porous,  solid,  and  impenetrability  may  be  taken  as 
instances.  It  is  by  no  means  necessary  that  the  pupil 
should  be  able  to  give  an  exact  and  comprehensive  sci- 
entific definition  of  such  terms;  a  few  analytical  ques- 

10 


218  HOW  TO  TEACH 

tions  by  the  teacher  will  readily  show  if  the  subject  is 
understood. 

When  a  lesson  from  the  text-book  is  to  be  given  for 
home  study,  it  should  first  be  carefully  illustrated  and 
explained.  No  teacher  will  be  likely  to  do  tbis  as  well 
as  he  should,  if  he  give  the  subject  no  thought  until 
about  to  assign  the  lesson.  After  receiving  these  expla- 
nations the  pupil  will  be  far  less  liable  to  misconceive 
or,  as  sometimes  happens,  to  fail  utterly  to  comprehend 
the  statements  of  the  text.  As  far  as  the  subject  will 
allow,  he  should  be  led  through  the  medium  of  experi- 
ment to  a  knowledge  of  the  facts.  The  facts  once  as- 
certained, the  principles  underlying  them  may  be  de- 
duced. A  limit  will,  sooner  or  later,  be  reached,  where 
the  more  recondite  parts  of  the  subject,  so -far  as  they 
may  be  entered  upon,  must  be  taught  empirically,  in 
consequence  of  tbe  pupil's  limited  knowledge  of  other 
departments  of  science. 

For  instance,  suppose  that  the  teacher  has  already 
experimentally  established  in  his  pupil's  mind  a  general 
idea  of  the  terms  force  and  gravity,  and  that  he  now 
wishes  to  lead  him  to  know  that  "  the  weight  of  a  body 
is  the  measure  of  i\\&  force  of  gravity"  acting  upon  it, 
and  after  that  to  establish  the  law  of  its  variation. 
Let  the  teacher  or  one  of  the  pupils  borrow  a  common 
spring-scale — the  smaller  and  simpler  the  better — let  a 
pupil  pull,  and  at  the  same  time  notice  that  he  is  ex- 
erting a  force,  that  the  position  of  the  index  will  vary 
with  the  degree  or  amount  of  force,  that  the  motion  is  in 
the  direction  of  the  force,  however  the  instrument  may 
be  held  ;  now  place  a  succession  of  heavy  bodies  in  the 
scale,  and  let  him  notice  that  the  effects  are  identical 
with  those  produced  by  his  muscular  force.  He  will 
no  longer  vaguely  conceive  that  the  effect  produced 


ELEMENTARY  SCIENCE.  219 

upon  the  scale  is  because  the  body  is  heavy  (which  was 
to  him  a  vague  term),  but  because  the  earth  actually 
pulls  it  as  he  did,  though  no  connecting  bond  is  visible, 
as  when  lie  pulled.  A  knitting-needle  suspended  and 
balanced  upon  a  thread  and  acted  upon  by  a  simple 
magnet,  will  clearly  convince  him  that  &  force  may  DP 
exerted  by  one  body  upon  another  without  actual  coiv 
tact.  You  have  clearly  defined  for  him  the  idea  that 
"  the  weight  of  a  body  is  the  measure  of  the  earth's  at- 
traction upon  it."  If  now  you  wish  to  teach  the  law 
of  the  variation  of  the  weight  of  a  body  of  invariable 
mass,  as  should  indeed  be  done,  the  next  step  must  be 
empirical.  The  pupil's  deficiency  in  mathematics  for- 
bids any  other  course  of  procedure.  The  "Law  of 
Gravitation  "  must  be  stated  to  him,  together  with  the 
reason  for  so  doing  without  proof.  It  will  develop  in 
many  a  mind  an  earnest  desire  to  supply  that  deficiency. 
The  law  of  the  variation  of  weight  may  now  be  readily 
deduced  by  first  adding  to  the  pupil's  mathematical 
knowledge  the  technical  meaning  of  the  term  square, 
and  then  giving  a  variety  of  simple  arithmetical  prob- 
lems to  illustrate  it. 

There  is,  perhaps,  no  graver  or  more  common  error 
in  relation  to  this  subject,  among  earnest  teachers  who 
are  called  upon  to  teach  it,  than  the  notion  that  this 
requires  expensive,  or  complicated  apparatus.  The  very 
contrary  is  ihe  case  in  the  great  majority  of  instances. 
Expensive  apparatus,  with  its  show  of  brass  and  glass, 
has  a  direct  tendency  to  repress  the  most  precious  ele- 
ment and  evidence  of  a  teacher's  success — experiment- 
ing at  home  by  the  pupils  themselves.  The  principles 
of  the  lever  may  be  just  as  well  developed  by  means  of 
a  pen-handle,  a  pointer,  or  a  window-pole,  as  by  a  pol- 
ished brass  or  steel  bar ;  a  large  spool  makes  an  excel- 


220  HOW  TO   TEACH 

lent  wheel  and  axle;  a  ribbon-block  ti  good  single  pul- 
ley, fixed  or  movable ;  a  slate,  a  book,  or  a  shingle,  an 
inclined  plane  ;  a  pocket-knife  will  soon  furnish  a  good 
wedge  from  a  little  piece  of  board,  while  the  use  of  the 
blade  itself  is  an  excellent  illustration  of  the  applica- 
tion of  the  principle;  and  a  large  screw  or  a  discarded 
auger-bit,  with  a  knitting-needle  or  a  pen-holder  for  a 
lever,  makes  an  efficient  single  screw.  And  so  through 
every  department  of  the  subject.  Nothing  marks  more 
fully  the  ability  of  a  teacher  than  fertility  in  such  re- 
sources. Strings,  tops,  balls,  and  marbles;  ^op-guns, 
potato-mills,  bean-shooters,  and  putty-blowers,  and  the 
thousand  and  one  nameless  articles  to  be  found  in  pu- 
pils' pockets,  furnish  an  exhaustless  mine  of  apparatus, 
and  good  apparatus  too,  for  the  skillful  teacher.  The 
immortal  Dalton  wrought  out  his  atomic  chemical  the- 
ory with  apparatus  which  may  be  excelled  in  many  a 
junk  or  old  bottle  shop  ;  and  the  teacher  determined  to 
succeed  will  find  that  "where  there  is  a  will  there  is  a 
way." 

SYLLABUS  OF  TOPICS. 

(To  be  illustrated  as  far  as  possible  objectively.) 

CONSTITUTION,  FOUMS,  AND  PROPERTIES  OF  MATTER. — Illus- 
trate the  following  terms — body  or  mass,  molecule,  atom  ;  solid, 
fluid,  liquid,  gas;  sensible  or  cellular  pores,  as  in  bread  or 
sponge  ;  physical  or  intermolecular  pores,  as  iu  iron,  water,  air, 
and  every  form  of  matter ;  porosity. 

Extension,  impenetrability,  rarity  and  density,  compressibil- 
ity and  expansibility,  inertia,  mobility. 

FORCE  AND  ITS  FOKMS. — Attraction  and  repulsion:  refer  brief- 
ly to  the  fact  that  atoms  and  atomic  forces  are  treated  of  in  chem- 
istry. Indestructibility  of  matter  to  be  briefly  explained. 

MOLECULAR  FORCES. — Cohesive  force :  the  properties  of  matter 
which  are  dependent  upon  cohesion  ;  tenacity,  flexibility,  brittle- 
ness,  hardness,  ductility,  malleability;  the  properties  depend- 


ELEMENTARY  SCIENCE.  22 1 

ent  upon  cohesion  and  molecular  repulsion ;  elasticity.  Illustrate 
the  elasticity  of  flexure ;  of  compression ;  of  expansion  ;  of  tor- 
sion. Relations  of  solids,  liquids,  and  gases  to  molecular  attrac- 
tion and  repulsion. 

Adhesive  force :  properties  dependent  upon  adhesion;  capil- 
lary attraction  and  its  uses  iu  organic  and  inorganic  nature. 

Din&iMity  of  matter — in  to  particles  by  mechanical  force;  into 
molecules  by  heat,  solution,  etc. — What  forces  are  overcome  in 
each  case,  and  by  what  other  force. 

MECHANICAL  FORCE. — Gravity — why  called  universal  gravita- 
tion; its  simplest  phenomena;  its  law;  weight,  a  measure  of 
gravity. 

MECHANICS  OF  SOLIDS. — Center  of  gravity;  line  of  direction, 
plumb-line ;  stable,  unstable,  and  indifferent  equilibrium. 

Simple.  Machines. — Lever,  with  simple  problems  in  mental 
arithmetic  ;  pulley,  wheel-and-axle,  inclined  plane,  wedge, screw. 

MECHANICS  OF  LIQUIDS  (Hydrostatics). — Mobility  of  liquids, 
and  its  cause;  their  small  compressibility;  pressure  in  every 
direction  ;  gravity  the  primary  cause ;  equality  of  pressure  at  a 
given  point ;  variation  of  pressure  with  depth  ;  meaning  of  the 
term  level;  why  still  water  has  a  level  surface;  why  the  hy- 
drant water  flows  from  the  open  tap  ;  at  what  height  it  ceases  to 
flow,  and  why  ;  other  illustrations  of  the  same  principle ;  what 
that  principle  is ;  the  hydrostatic  paradox ;  the  hydraulic 
press;  specific  gravity;  the  hydrometer;  why  iron  ships  float. 

MECHANICS  OF  OASES  (Pneumatics). — Air — its  compressibility, 
expansibility,  and  elasticity;  chief  mechanical  difference  from 
liquids;  its  weight ;  its  pressure  in  all  directions  ;  upward  press- 
ure and  how  shown  ;  the  mercurial  barometer,  its  construction, 
principle,  and  uses;  Torricelli's  experiment;  Pascal's  experi- 
ment ;  the  aneroid  barometer ;  height  of  the  atmosphere,  and 
gradual  diminution  of  its  density. 


Astronomy* — The  teacher  should,  at  first,  en- 
deavor to  awaken  an  interest  in  the  subject  by  referring 
to  some  of  the  most  impressive  and  beautiful  phenom- 
ena connected  with  the  sun,  the  moc.i,  the  stars,  planets, 


222  HOW  TO  TEACH. 

comets,  and  -meteors.  He  should  endeavor  to  induce 
the  pupils  to  observe  more  attentively  these  phenomena, 
and  to  excite  their  curiosity  to  know  about  them.  En- 
courage them  to  ask  questions  in  relation  to  what  they 
observe ;  as,  Why  does  the  moon  change  its  appearance  ? 
Why  does  the  sun  rise  so  far  from  the  east  point,  or  set 
so  far  from  the  west  point  at  certain  times  in  the  year? 
What  bright  star  was  in  the  west  on  a  certain  night,  at 
a  particular  time  ?  and  other  such  questions,  some  of 
which  the  pupils  are,  of  course,  to  be  told  cannot  be 
answered  until  they  have  further  studied  the  subject. 
Thus  they  will  learn  to  study  the  science  from  nature 
as  well  as  from  the  book. 

Let  the  general  phenomena  of  the  heavens  be  first 
explained ;  the  movements  of  the  sun,  moon,  stars,  and 
planets  in  relation  to  the  horizon;  the  circles  of  daily 
motion  ;  the  difference  between  planets  and  fixed  stars ; 
how  to  distinguish  some  of  the  former,  etc. 

The  following  topics  may  then  be  taken  up  in  their 
order:  The  Earth,  its  form,  magnitude,  motions,  etc. ; 
Circles,  and  angular  distances  on  the  Earth  and  in  the 
heavens;  Day  and  Night /  the  Seasons,  etc:  these  topics 
should  be  illustrated  by  the  use  of  a  Tellurian,  and 
Problems  for  the  Globe  should  be  used  for  the  purpose 
of  exercise  and  illustration. 

Next,  teach  the  general  arrangement  of  the  Solar 
System.  Inferior  and  superior  planets — their  magni- 
tudes, revolutions,  position  of  orbits,  periodic  times, 
and  apparent  motions. 

The  mathematical  definitions  necessary  for  the  prop- 
er understanding  of  this  portion  of  the  subject  should 
be  taught  incidentally  thereto. 


FIEST    GEADE. 

Time  allowed,  about  twelve  months. 
OUTLINE   COUKSE. 


LANGUAGE. 

Heading,  Spelling,  Definitions,  and  Word  Anal- 
ysis, continued  as  in  the  preceding  grade. 

English  Grammar. — Analysis,  Parsing,  and  Syntactical 
criticism  and  correction,  continued;  the  anomalous  and  idio- 
matic forms  to  be  taught  and  explained. 

Composition. — Exercises  on  selected  themes;  Practice  in 
Letter  Writing,  commercial  and  social. 

MATHEMATICS. 

Mental  and  Written  Arithmetic. — Continued  and  re- 
viewed, including  the  rules  pertaining  to  the  mensuration  of 
regular  plane  surfaces  and  solid  bodies  ;  with  exercises  in  anal- 
ysis and  calculation,  continued. 

Algebra.—  Through  equations  of  the  first  degree. 

Geometry.— The  geometry  of  plane  figures,  with  practical 
applications. 

GEOGRAPHY  AND  HISTORY. 
Geography.— The  Outlines  of  Physical  Geography. 
History.— The  Outlines  of  Ancient  and  Modern. 


224  SOW  TO  TEACH 

ELEMENTARY  SCIENCE. 

BY  ORAL  INSTRUCTION,  OR  WITH  A  SIMPLE  TEXT  BOOK. 

Natural  Philosophy. — Simple  outlines  completed,  to  in- 
clude Acoustics,  Pyronomics,  Optics,  Magnetism,  and  Electricity. 

Astronomy. — Elementary,  continued  and  completed. 
Cliemistry. — Elementary  principles  and  facts. 

WRITING  AND  DRAWING. 

Penmanship. — Instruction  to  be  continued  as  in  the  preced- 
ing grade,  with  practice  in  the  writing  of  paragraphs,  verses, 
business  forms,  notes,  superscriptions,  etc. 

Dratving. — Drawing  objects  of  regular  form  in  perspective, 
block  combinations,  etc.,  with  shading;  copying  pictures  of  fami- 
liar objects,  animals,  etc. ,  with  easy  landscapes,  as  far  as  the 
time  may  permit ;  also  (for  males)  simple  architectural  arid  me- 
chanical drawing.  The  drawing  of  designs  to  be  continued. 

MISCELLANEOUS  BRANCHES. 

Book-7ceeping. — Single  and  double  entry ;  with  careful  in- 
struction in  the  principles  of  the  latter. 

Constitution  of  the  United  States. — History  of  its  adop- 
tion ;  its  various  provisions  and  amendments ;  the  reasons  for 
the  same  to  be  explained  as  far  as  may  be  necessary  or  appro- 
priate. 


GRAMMAR.  335 


How  TO  TEACH 


SUBJECTS     OP     THE     FIRST     GKADE. 


LANGUAGE. 

Reading,  Spelling,  and  Definitions* — See 

the  preceding  grade. 

English  Grammar. — The  exercises  of  this 
grade  comprise  those  of  analysis,  parsing,  and  com- 
position. Sentences  of  an  irregular  or  idiomatic  con- 
struction, should  be  presented  to  the  pupil,  with  the 
view  to  show  how  far  their  analysis  can  he  made  to 
harmonize  with  the  usual  syntactical  rules,  and  to 
teach  the  just  limits  of  their  use.  Anything  bordering 
on  slang  should  be  discountenanced  and  condemned. 
An  improper  construction — that  is,  one  that  contra- 
venes well-established  rules  and  principles — should  not 
be  sanctioned  by  any  ingenious  analytical  contrivance 
or  substitution. 

The  exercises  in  analysis  should  embrace  the  careful 
and  critical  study  of  select  passages  from  some  of  the 
best  English  and  American  writers ;  as  Shakespeare, 
Milton,  Pope,  Cowper,  Young,  Bryant,  Longfellow,  etc., 
etc.  Prose  writers,  such  as  Addison,  Johnson,  Irving, 
etc.,  should  also  be  drawn  upon  for  exercises, — always, 
however,  with  a  critical  end  in  view, — to  discover  and 
correct  errors,  as  well  as  to  find  excellencies  and  beauties. 

Such  exercises,  to  however  limited  an  extent  it  is 
10* 


22G  HOW  TO  TEACH 

possible  to  carry  them,  will  always  exert  an  important 
influence  upon  the  pupils'  style  of  composition,  if  not  of 
daily  speech.  They  will  serve,  moreover,  to  cultivate  the 
taste  of  the  pupils,  and  to  awaken  an  interest  in  their 
minds  in  the  study  of  English  and  American  literature. 
A  good  reading-book  will  be  found  an  important  auxili- 
ary in  carrying  on  the  instruction  here  suggested. 

Composition. — The  exercises  in  composition  in 
this  grade,  as  in  those  preceding  it,  should  be,  to  some 
extent,  impromptu,  s"o  us  to  develop  that  fluency  and 
readiness  in  the  written  expression  of  thought  which  is 
of  so  much  service  in  almost  every  sphere  of  life.  The 
writing  of  letters,  etc.,  as  suggested  in  the  outline 
course,  should  receive  a  very  careful  attention  at  this 
stage  of  the  pupils'  progress. 


MATHEMATICS. 

Arithmetic. — In  this  grade,  the  teaching  of  arith- 
metic consists  in  large  part  of  a  review  of  what  has 
gone  before,  with  exercises  sufficient  in  number  and  dif- 
ficulty to  familiarize  the  pupils  with  the  principles,  and 
render  them  expert  and  accurate  in  their  application. 
For  suggestions  in  regard  to  this  part  of  the  work,  the 
teacher  is  referred  to  the  preceding  grades. 

The  advanced  work  should  comprise  the  following: 
Exchange,  Equation  of  Payments,  Proportion,  Partner- 
ship, Square  Root,  and  Cube  Root,  with  their  simple 
applications,  and  Mensuration.  The  exercises  em- 
ployed to  teach  these  departments  of  arithmetic,  should 
be  of  as  practical  a  character  as  possible ;  and  all  the 
processes  should  be  specially  analyzed,  the  rules  given 


ARITHMETIC.  22? 

being  in  all  cases  deduced  from  the  analysis.  A  careful 
explanation  of  the  business  transactions  involved  in  any 
of  the  rules  or  their  applications,  should  always  be  given 
before  the  pupils  are  required  to  solve  the  problems. 
Failure  more  frequently  arises  from  a  want  of  this  knowl- 
edge than  from  a  deficiency  in  arithmetical  attainment. 

The  following  syllabus  contains  a  brief  summary  of 
what  is  suggested  to  be  taught  in  this  grade. 

SYLLABUS  OP  TOPICS. 

EXCHANGE.  Its  nature  ;  bills  of  exchange;  par  of  exchange; 
acceptance;  domestic  exchange — to  include  two  cases: — 1.  To 
find  the  cost  of  a  draft  when  its  face  and  the  rate  are  given  ;  2. 
To  find  the  face,  the  cost  and  rate  being  given  ;  foreign  exchange 
— including  the  consideration  of  bills  on  England  and  France 
(cases  as  in  domestic  exchange) ;  analysis  as  in  percentage. 

NOTE.— Remember  that  the  old  par  value  of  the  ponnd  sterling  is  now 
prohibited  by  law,  and  that  the  newle^al  value  is  $4.866^. 

EQUATION  OF  PAYMENTS.  Cases : — 1.  To  find  the  average  time 
of  payment,  when  the  items  have  the  same  date,  but  different 
credits ;  2.  When  the  items  have  different  dates  ;  3.  To  find  the 
average  time  for  paying  balance  of  account,  having  both  debits 
and  credits.  Analysis,  on  the  principal  of  interest,  reducing  each 
principal  concerned  to  $1. 

PROPORTION.  Ratio  ;  proportion  defined ;  relation  of  ante- 
cedents and  consequents  ;  ratio  of  4  to  12,  4  :  12=-,%;  method  of 
finding  the  missing  term ;  simple  and  compound  proportion  dis- 
tinguished ;  problems  involving  each :  these  problems  should 
he  only  such  as  are  required  to  illustrate  the  principle,  since 
they  are  ordinarily  to  be  solved  by  analysis  previously  given. 

PARTNERSHIP.  Terms  defined.  Cases  : — 1.  To  find  each  part- 
ner's share  when  the  profit  or  loss  is  divided  according  to  capital 
only  ;  2.  To  find  it  when  time  is  considered.  Analysis,  fractional, 
or  by  means  of  proportion. 

SQUARE  ROOT.  Involution  and  evolution  defined  :  simple 
examples  of  each;  powers  of  roots;  illustration  of  what  is 
meant  by  finding  the  square  of  a  number;  what  is  meant  by 


228  SOW  TO  TEACH 

square  root.  Illustrate  by  simple  powers,  integral  and  fractional — 
common  fractions  and  decimals  (the  latter  carefully).  Problems 
in  which  the  root  contains  denominations  other  than  units.  Illus- 
trate by  geometrical  construction  (square  of  the  sum  of  two  lines). 

The  following  are  specimens  of  "  simple  applications,"  which 
should  be  taught  in  this  grade : — Given  the  area,  to  find  the  side 
of  the  square  containing  it. 

Given  the  length  and  width  of  a  rectangle,  to  find  the  side  of 
a  square  equivalent  to  it. 

NOTE.— In  teaching  the  pupils  how  to  find  the  area  of  a  rectangle,  avoid 
giving  the  erroneous  impression  that  we  absolutely  multiply  the  length  by 
the  width,  as  expressed  by  denominate  numbers.  Show  that  the  number  of 
superficial  units  corresponding  to  the  linear  units  of  the  length,  is  multiplied 
by  the  number  (abstract)  of  linear  units  in  the  width.  Thus,  if  the  length  be 
10  feet,  and  the  width  5  feet,  Ihe  area  must  be,  not  5  feet  times  10  feet,  but 
5  times  10  square  feet,  equal  to  50  square  feet. 

Given  any  two  sides  of  a  right-angled  triangle,  to  find  the 
other  side.  Teach  and  illustrate  the  geometrical  theorem  on 
which  this  problem  depends.  Give  various  questions  requiring 
an  application  of  this  problem. 

CUBE  ROOT.  How  to  extract  it,  with  an  illustration  of  the 
process.  This  is  best  given  by  means  of  the  blocks  constructed 
for  that  purpose.  If  the  pupil  has  studied  Algebra  sufficiently, 
a  demonstration  by  the  Binomial  Theorem  may  be  given.  The 
formula  representing  the  cube  of  the  sum  of  two  quantities,  will 
enable  the  pupil  to  remember  clearly  the  details  of  the  rule. 

The  applications  of  the  Cube  Root  should  include  the  com- 
putation of  the  contents  of  similar  solids. 

MENSURATION.  This  should  at  least  include  the  following 
cases:—!.  To  find  the  area  of  a  parallelogram  when  the  base 
and  altitude  are  given ;  2.  To  find  the  area  of  other  quadri- 
laterals, with  sufficient  data  ;  3.  To  find  the  area  of  triangles ; 
4.  To  find  the  area  of  a  circle ;  5.  To  find  the  diameter  and 
circumference  of  a  circle  when  the  area  is  given  ;  6.  To  find  the 
solid  contents,  from  sufficient  data,  of  a  cube,  parallelepiped, 
prism,  pyramid,  cylinder,  cone,  and  sphere  ;  7.  To  find  the  con- 
tents of  a  cask,  or  other  vessel,  with  the  requisite  data. 

Every  topic  to  be  treated  in  the  arithmetic  of  this 
grade  should  be  introduced  by  corresponding  mental 
exercises,  the  slate  being  used  only  when  the  numbers 


ALGEBRA.  229 

involved  are  too  large  to  be  readily  retained  in  the  mind. 
The  pupils  should  be  very  frequently  practiced  in  this 
mental  work.  The  text-book  in  mental  arithmetic  should 
be  sparingly  used,  and  great  care  should  be  exercised  in 
assigning  lessons  for  home-study  in  this  branch. 

Algebra. — This  subject  should  be  taught  as  a  pe- 
culiar mathematical  language,  by  means  of  which  the 
relations  of  quantities  and  the  results  of  their  combina- 
tions may  be  expressed,  and  thus  the  reasoning  in  re- 
gard to  them  facilitated.  The  symbols,  both  of  quanti- 
ties and  relations,  or  operations,  should  at  first  be  care- 
fully taught  and  illustrated. 

The  simple  operations  of  addition,  subtraction,  mul- 
tiplication, and  division,  should  not  be  exhaustively 
treated,  as  is  usually  done,  before  the  pupil  is  made 
acquainted  with  the  nature  and  use  of  equations.  The 
equation  is  to  algebra  what  the  proposition  is  to  ordi- 
nary language.  It  is  the  means  of  definitely  expressing 
a  mathematical  truth,  either  particular  or  general.  In- 
equations (technically  so  called)  express  truth's,  but  not 
exactly;  as,  when  we  say,  x  +  yyo,  we  do  not  indicate 
how  much  the  sum  of  a;  and  y  exceeds  5  ;  but  if  we  say, 
x  +  y=G,  we  express  a  precise  fact.  It  is  suggested, 
therefore,  that  equations  be  presented  very  soon  after 
the  preliminary  explanation  of  the  symbols  employed. 
The  examples  of  equations  first  presented  should  be  of 
the  simplest  character  ;  and  their  use  in  the  solution  of 
problems  should  be  objectively  shown.  This  may  be 
done  by  employing  a  few  very  easy  questions,  such  as 
are  given  in  some  of  the  text-books,  for  mental  solution  ; 
as,  What  number  is  that,  to  the  half  of  which  if  5  be 
added  the  sum  will  be  11  ?  Even  the  dullest  pupil  can 
be  easily  made  to  perceive  the  use  of  expressing  that 


230  UO W  TO  TEACH 

condition  so  that  it  can  be  clearly  kept  in  view ;  as  (x 
representing  the  unknown  number)  f +  5  =  11. 

In  solving  such  a  problem,  the  successive  steps  or  pro- 
cesses of  reasoning  should  be  kept  in  view.  Thus,  sub- 
tracting 5  from  each  member,  the  result  (expressed  by  a 
second  equation)  is,  |— 6;  and,  multiplying  by  2  the 
result  (expressed  by  a  third  equation)  is  x=l2,  which 
gives  the  solution.  (Applied  axiom  to  be  referred  to.) 

Such  an  exercise,  properly  performed,  will  develop 
more  intelligence  than  whole  months  of  mechanically 
working  out  by  blind  rules  long  sums  in  addition, 
subtraction,  multiplication,  and  division,  such  as  Multi- 
ply xs — 3x  +  5  by  x3 — x*  +  2  ;  Divide  xs — f  by  x — y,  etc., 
etc.  These  exercises  are  proper  in  their  place,  but  of 
themselves  they  have  but  little,  if  any,  educational  or 
practical  value. 

SYLLABUS  pp  TOPICS. 

1.  Preliminary  explanation  of  symbols,  both  Utters,  as  repre- 
sentatives of  quantity,  and  the  signs  of  relation  or  operation,  as, 
+  —  x  -r-  =  etc. ;  exercises  to  familiarize  the  pupil  with  their 
significance  and  the  mode  of  reading  them. 

NOTE.— It  will  be  of  great  service  to  accustom  the  pupil  to  read  algebraic 
expressions  in  such  a  way  as  at  once  to  indicate  their  meaning ;  as,  a  4  b,  the 
the  sum  of  a  and  b:  a—b,  the  difference  between  a  and  b-  ax&,  the  product 
of  a  and  b,  etc.  Exercises  in  finding  the  numerical  value  of  expressions, 
when  particular  values  are  attributed  to  the  representative  letters,  will  greatly 
aid  in  accomplishing  this  result.  Thus,  find  the  value  of  a2b — 63  when  a=3, 
6=2,  c=l,  etc.  c 

2.  Easy  problems  in  arithmetic,  the  solutions  of  which  may 
be  facilitated  by  the  use  of  equations,  the  latter  to  be  of  the 
simplest  form,  and  involving  only  an  application  of  the  pupil's 
acquired  knowledge  of  symbols.     This  will  at  once  show  the 
pupils  the  value  of  the  algebraic  notation,  and  interest  them  in 
the  study  of  the  subject,  as  being  of  practical  value. 

8.  Mental  practice  in  solving  such  problems,  by  means  of  equa- 
tions. Most  of  the  text-books  in  use  will  afford  a  sufficient  variety. 


ALGEBRA.  231 

4.  Practice  in  solving  equations  of  this  character  ;  each  equa- 

x        x 

tion  to  be  read  previously  in  the  form  of  a  problem  ;  as  ---  = 

3        8 
10  ;  which  may  be  read  : 

What  number  is  that  one-third  of  which  exceeds  one-eighth 
of  it  by  10? 

The  method  of  clearing  equations  of  fractions  and  transposition 
should  be  taught,  not  by  applying  mechanical  rules,  but  as  pro- 
cesses of  analytical  reasoning.  Thus  in  the  equation  above 
given,  the  pupil  will  easily  be  made  to  perceive,  that  the  multi- 
plication of  both  members  by  24  will  produce  an  equation  with- 
out fractions. 

24x       24x 

(The  intermediate  step  ---  =  240  should  be  at  first  used.) 
3          8 

5.  After  the  pupils  have  acquired  a  clear  idea  of  the  nature 
and  use  of  equations,  and  some  expertness  in  operating  with 
those  of  a  simple  character,  those  of  a  more  difficult  or  complex 
form   should  be  preseuted,  giving  occasion  for  the  use  of  the 
operations  of  addition,  subtraction,  multiplication,  and  division, 
which  can  then  be  more   exhaustively  treated,  with  sufficient 
practice  on  the  part  of  the  pupil. 

6.  The  nature  of  literal  equations  or  general  expressions  should 
be  then  taught,  and  examples  given,  some  of  which  may  be 
made  to  involve  an  application  of  all  these  processes. 

Such  as  the  following  are  suggested: 

x  +  a        x  —  a 

(l.)   -  -  =  d 

b  c 

x  —  a        x  —  b 
(2.)    -  + 


(3.) 
(4.) 


b  a 

x—  a*        x  —  b2 


a  —  b  a  +  b 
(a  +  b)  x        (a  —  b)  x 
(5.)    - 

a  —  b  a  +  b 


232  HOW  TO  TEACH 

Such  equations  as  the  above  iuvolve  much  useful  practice,  not 
only  in  adding,  subtracting,  multiplying,  and  dividing,  but  also 
in  fractions  and  in  factoring.  The  latter  should  receive  careful 
attention. 

6.  The  method  of  solving  equations  containing  more  than  one 
unknown  quantity — involving  the  various  mei  bods  of  elimination 
— should  follow  this,  and  sufficient  practice  in  the  solution  of  prob- 
lems should  also  be  afforded.  The  latter,  with  the  preparation 
herein  indicated,  may  be  made  a  most  important  aid  in  training 
the  mind  to  careful  and  exact  analysis,  and  logical  reasoning — 
perhaps  the  most  important  object,  generally,  of  the  study  of 
this  subject. 

NOTE. — This  syllabus  is  not  designed  to  be  entirely  exhaustive,  but  to  afford 
hints  as  to  the  order  and  method  of  presenting  the  most  important  topics. 

Geometry. — This  subject,  from  its  extremely  ab- 
stract character,  is  quite  difficult  for  young  students 
fully  to  comprehend.  It  is  essential  that  the  abstract 
ideas  with  which  it  is  concerned  should  be  developed 
in  the  minds  of  the  pupils  at  the  preliminary  stage  of 
the  study.  Unless  this  is  done,  they  cannot  be  bene- 
fited by  the  instruction,  nor,  indeed,  take  any  interest 
in  it.  They  will,  moreover,  be  wholly  incapable  of 
carrying  on  the  processes  of  reasoning  involved  in  the 
demonstrations,  unless  they  clearly  apprehend  the  na- 
ture of  the  truths  to  be  proved,  as  well  as  of  those  as- 
sumed as  premises,  or  arguments. 

The  first  idea  to  be  developed  is  that  of  a  solid,  as 
conceived  in  geometry,  involving  three  dimensions  of 
extension;  next,  that  of  a  surface,  abstracted  from  the 
solid,  involving  two  dimensions  ;  next,  that  of  a  line,  ab- 
stracted from  the  surface,  involving  one  dimension; 
and,  lastly,  that  of  a  point,  as  indicative  of  a  position 
in  the  line,  or  at  either  of  its  extremities,  and  involving 
no  dimensions.  These  terms,  reversing  the  order,  should 
then  be  defined ;  namely,  point,  line,  surface,  solid. 


GEOMETRY.  333 

Unless  these  fundamental  conceptions  are  clearly  and 
thoroughly  impressed  upon  the  minds  of  the  pupils, 
no  true  progress  can  be  made. 

The  classification  of  lines  and  surfaces  may  then  be 
taught,  the  fundamental  idea  used  being  that  of  direc- 
tion ;  as  of  a  straight  line,  never  changing  its  direction ; 
a  curve  line,  changing  it  at  every  point ;  of  a  broken 
line,  changing  it  at  certain  points.  The  classification 
of  surfaces  into  plane,  curved,  and  broken  may  be  made 
in  an  analogous  manner. 

With  this,  the  idea  of  parallel  lines  may  be  made  to 
harmonize  by  conceiving  them  as  lying  side  by  side 
(literal  meaning  of  parallel),  and  all  in  the  same  direc- 
tion, i.e.,  tending  to  a  point  at  an  infinite  distance,  or 
tending  to  points,  at  a  finite  distance,  which,  wherever 
assumed,  are  at  the  same  distance  from  each  other  (the 
latter  may  be  the  easier  to  develop  at  first). 

The  idea  of  a  plane  angle  should  be  made  to  harmo- 
nize with  these  conceptions  of  a  straight  line  and  par- 
allel lines,  being  conceived  as  expressing  the  difference 
in  direction  of  two  straight  lines  that  meet  at  a  point. 

NOTE— This,  it  will  be  seen,  harmonizes  with  the  idea  of  parallel  lines, 
which  tend  to  a  point  at  an  infinite  distance,  and  hence  never  meet,  and  can- 
not form  an  angle;  while  the  straight  lines  that  form  an  angle  tend  to  a  point 
at  a  finite  distance,  and  meeiing  at  that  point,  form  the  angle. 

The  definitions  of  Geometry  form  the  groundwork  of 
the  subject,  constituting  the  basis  upon  which  all  the 
subsequent  reasoning  rests;  hence,  it  is  very  important 
that  these  definitions  should  be  clearly  understood  and 
carefully  committed  to  memory. 

It  is  desirable,  before  the  pupils  are  required  to  study 
demonstrations,  that  the  different  methods  of  reasoning 
should  be  carefully  explained,  and  that  they  should,  to 
some  extent,  be  exercised  in  the  same.  This  can  easily 
be  done  by  bearing  in  mind  that  geometrical  truths 


234  HO  W  TO  TEACH 

have  reference  to  a  comparison  of  magnitude,  and  hence 
involve  the  idea  of  equality  as  a  definite  fact,  and  ine- 
quality indefinitely.  Thus,  it  is  required  to  be  proved 
that  the  sum  of  the  three  angles  of  a  triangle  is  equal 
to  two  right  angles ;  also,  that,  of  any  two  sides  of  a 
triangle,  that  which  lies  opposite  to  the  greater  angle 
is  greater  (nut  how  much  greater).  Hence,  as  a  pre- 
liminary exercise,  the  following  might  be  given : — 
Question — If  A  is  equal  to  B,  and  B  is  equal  to  C,  how 
does  A  compare  with  C?  Answer — They  are  equal. 
Question — Why  is  A  equal  to  C  ?  Answer — Because 
they  are  both  equal  to  B.  Question — How  does  that 
prove  it  ?  Answer — Because  things  that  are  equal  to 
the  same  thing  are  equal  to  each  other.  Question — 
Can  that  be  proved?  Answer — It  cannot;  it  is  self- 
evident.  Question — What  are  self-evident  truths  called  ? 
Answer — They  are  called  axioms. 

A  variety  of  such  exercises  maybe  employed;  and, 
in  this  way,  the  pupil,  before  beginning  formal  demon- 
strations, may  be  made  clearly  to  apprehend  the  nature 
of  geometrical  reasoning — so  different  from  that  which 
he  has  generally  employed  during  all  his  previous  stud- 
ies, or  which  he  is  accustomed  to  use  in  daily  life.  If 
the  foundation,  as  here  suggested,  is  well  laid,  the  pupil 
will  soon  find  it  as  easy  a  task  to  read  his  geometry, 
and  to  learn  it  by  reading  (not  role  study],  as  to  read 
any  other  book  of  science. 

Of  course,  in  hearing  recitations  in  geometry,  the 
teacher  should  vary  the  method,  so  as  to  preclude  en- 
tirely the  possibility  of  any  rote  study,  or  merely  verbal 
recitation.  For  this  purpose,  the  figures  employed 
should  be  different  from  those  in  the  text  book,  the 
letters  used  in  connection  with  the  figures  should  be 
changed,  or  numerals  used  in  their  stead.  The  demon- 


GEOMETRY.  335 

strations  should  sometimes  be  given  without  using 
either  letters  or  numerals ;  and,  in  the  case  of  such  as 
are  very  easy,  the  figures  themselves  may  be  dispensed 
with.  In  most  cases,  the  pupil  should  be  required 
briefly  to  recapitulate  the  arguments  employed. 

The  amount  of  ground  to  be  covered  in  this  grade  is 
denned  as  the  "  Geometry  of  Plane  Figures."  The  fol- 
lowing Syllabus  (intended  to  be  only  suggestive)  em- 
braces everything  required. 

SYLLABCS  OF  TOPICS. 

I.  Elementary  definitions — axioms — symbols. 

II.  Theorems  relating  to  straight  lines,  angles,  and  polygon..  : 

1.  The  sum  of  any  two  adjacent  angles  is  equal  to  two  right  angles. 

2.  Vertical  angles  are  equal  to  each  other.    3.  The  various  theo- 
rems pertaining  to  the  angles  formed  by  the  intersection  of  two 
parallel  lines  and  a  third  line.     4.  Angles  having  their  sides 
parallel  are  equal.     5.  Triangles  are  equal,  («)  when  they  have 
two  sides  and  the  included  angle  in  each  respectively  equal ;  (b) 
when  they  have  two  angles  and  the  interjacent  side  in  each  re- 
spectively equal;  (c)  when  they  have  three  sides  in  each  respec- 
tively equal.     6.  The  sum  of  the  three  angles  of  a  triangle  is 
equal  to  two  right  angles.     7.  The  sum  of  the  interior  angles  of 
a  polygon  is  equal  to  twice  as  many  right  angles  as  the  figure 
has  sides,  less  four  right  angles.     8.  The  sum  of  the  exterior 
angles  of  a  polygon  is  equal  to  four  right  angles.     9.  Theorems 
relating  to  a  comparison  of  the  perpendicular  and  oblique  line 
drawn  from  the  same  point  to  the  same  straight  line.     10.  Only 
one  perpendicular  can  be  drawn  from  a  given  point  to  a  given 
straight  line.     11.  The  greater  side  of  any  triangle  is  opposite  to 
the  greater  angle ;  and  the  converse.    12.  The  opposite  sides  and 
angles  of  a  parallelogram  are  equal ;  and  the  converse.    13.  Any 
problem,  either  after,  or  in  connection  with,  these  theorems, 
which  can  readily  be  performed ;  as,  to  construct  an  equilateral  tri- 
angle, to  bisect  a  given  straight  line,  or  a  given  angle,  etc.    In 
order  to  aid  in  the  solution  of  these,  it  will  be  necessary  to  teach 
the  definition  of  a  circle,  its  construction,  and  parts. 

Compass  and  ruler  exercises  may  also  be  profitably  interspersed. 


23G  HOW  TO  TEACH 

III.  Ratio  and  Proportion. 

IV.  The  Circle: — 1.  Delations  of  angles  to  chords.    2.  Relations 
of  angles  to  arcs. 

V.  Area:  1.  Comparative  areas  of  parallelograms  and  of  trian- 
gles.    2.  Measure  of  areas,  of  a  parallelogram,  of  q  triangle,  of  a 
trapezoid,  etc.     3.  Of  squares  described  on  the  sides  of  triangles. 

VI.  Similarity  of  figures  :  1.  Of  triangles.    2.  Of  polygons. 

VII.  Problems,  pertaining   to  the  circle,  the  polygon,  area, 
and  similar  figures. 

VIII.  Practical  applications  in  mensuration.  (See  arithmetic.) 

Outlines  of  Physical  Geography. — Some 
departments  of  physical  geography,  though  perhaps  not 
known  to  the  pupil  by  that  name,  have  always  been  the 
necessary  introductory  element  to  the  most  rudimentary 
outline  of  political  geography. — Describing  the  course 
of  a  river,  the  position  ot'a  peninsula  or  a  cape,  the  direc- 
tion of  a  mountain  chain,  or  the  boundaries  of  a  conti- 
nent, is  as  truly  a  part  of  physical  geography,  as  is  the 
explanation  of  the  oscillation  of  the  tropical  rain-belt, 
of  the  formation  and  transport  of  icebergs,  or  of  the 
theories  of  the  trade-winds  and  ocean-currents. 

The  physical  geography  specially  described  in  this 
grade  is  a  comparative  science.  It  considers  the  world 
as  an  organic  whole,  and  includes  the  study  of  its  plane- 
tary conditions,  of  the  mutual  relations  of  all  its  parts,  in- 
ternal and  external — the  land,  the  sea,  and  the  atmos- 
phere,— together  with  the  geographical  distribution  and 
conditions  of  the  various  forms  of  vegetable  and  animal 
life,  and  of  the  various  races  of  mankind. 

In  the  brief  time  that  can  be  allowed  to  so  compre- 
hensive a  subject  in  a  single  grade,  it  is  obvious  that 
only  the  simplest  outline  can  be  presented.  The  work 
has  been  carefully  prepared  for  in  the  geography  of  the 
preceding  grades,  to  which  attention  is  here  specially 
invited. 


PHYSICAL  GEOGRAPHY.  237 

A  synopsis  of  the  points  included  in  the  grade  is  here 
appended.  If  a  text-book  is  used,  the  teacher  should 
first  be  thoroughly  familiar  with  its  contents,  so  that  it 
may  be  employed  principally  as  a  reading  or  reference- 
book  from  which  appropriate  selections  may  be  read  in 
the  class.  If  any  other  course  be  pursued,  most  of  the 
text-books  treat  the  subject  so  extensively  that  the  pupil 
will  necessarily  leave  it,  at  the  end  of  the  term,  with 
only  an  unfinished  foundation  and  no  superstructure. 

SYLLABUS  OF  TOPICS. 

TJie  Earth  as  a  Globe — its  form  and  dimensions,  and  how  as- 
certained. 

The  Earth  as  a  Planet — the  zones,  and  their  causes. 

The  Interior  of  the  Earth — its  probable  condition,  and  how  in- 
ferred. (Treat  briefly.) 

The  Surface  of  tJie  Earth — its    division  into  land,  water,  and 
atmospheric  envelope;  the  laud  divided;  the  ocean  not;  co 
parative  extent  of  land  and  water. 

The  Land  Surface — (Omit  Geology).  Comparison  of  the  con- 
tinents in  their  direction,  contour,  elevations,  andarea  ;  compari- 
son of  the  great  mountain  systems  of  the  continents;  volca- 
noes ;  distribution  of ;  theories  of  volcanic  and  earthquake  phe- 
nomena (very  brief) ;  comparison  of  the  plateau  belts;  of  the  great 
plains ;  the  great  islands  and  archipelagoes,  their  distribution  and 
arrangement. 

NOTE.— To  illustrate  the  comparison  of  the  continents  by  the  several  elapses 
of  elevations,  give  upon  the  blackboard  rough  chalk  diagrams  of  sections  of  the 
continents. 

The  Ocean— its  subdivisions  and  great  areas  compared ;  its 
level ;  its  great  currents,  their  function  and  some  one  theory  of 
their  origin  (very  brief) ;  its  tides  and  waves,  and  their  effects. 
(Both  very  brief.) 

The  Atmosphere—  its  constituents  ;  vital  importance  of  its 
watery  vapor  and  its  carbonic  acid  to  plants  and  animals;  evap- 
oration from  the  ocean  surface,  especially  i'i  the  torrid  zone ; 
the  atmosphere  and  the  watery  vapor  as  the  Earth's  blanket. 


233  HO  W  TO  TEACH 

Tfie  Winds — the  trades,  and  counter-trades ;  theory  of  (very 
brief) ;  region  of  variable  winds — (very  brief) ;  the  winds  as  car- 
riers of  ocean  vapor  ;  solar  heat  the  great  cause  of  oceanic  aiid 
atmospheric  circulation. 

The  Great  Main-belt— its  annual  oscillations;  tropical,  rainy, 
and  dry  seasons  ;  the  mountains  as  condensers — illustrations. 

Drainage — the  river  systems  of  the  several  continents  com- 
pared ;  their  existence  and  direction  in  relation  to  the  winds  and 
mountain  ranges  ;  causes  and  location  of  deserts — illustration  ; 
lakes ;  snow  in  the  frigid  zone,  and  on  lofty  mountains  in  the 
torrid  zone ;  glaciers,  their  origin  and  motion  (very  brief) ;  ice- 
bergs, their  origin. 

Vegetation  (very  brief) — warmth  and  moisture  necessary  to  ; 
general  characteristics  of  tropical  vegetation  ;  examples  of  tropi- 
cal plants  ;  examples  of  plants  of  subtropical  and  temperate  re- 
gions; of  arctic  regions;  the  great  forest  belts,  their  location 
and  causes ;  prairie  belts ;  desert  belts  ;  effects  of  certain  plants 
on  human  industries  and  development  (very  brief). 

Animals  (very  brief) — comparison  of  the  characteristics  of  the 
several  zones  and  continents  as  to  animal  life  ;  examples. 

Man — the  various  races,  their  numerical  proportion,  leading 
peculiarities,  and  distribution. 

The  pictures  and  illustrative  diagrams  and  maps  of  any  good 
text-book  will,  if  properly  used,  very  greatly  simplify  and  expe- 
dite the  study  of  nearly  every  department  of  the  subject,  and 
will  render  definite  ideas  that  might  be  otherwise  vague. 


History  (Outlines  of  Ancient  and  Modern}. — The 
general  suggestions  given  in  relation  to  the  history  of 
the  United  States  (see  Third  Grade)  are,  to  a  very  great 
extent,  applicable  to  this  grade.  The  much  greater  ex- 
tent of  time  to  be  covered  in  teaching  ancient  and  mod- 
ern history,  together  with  the  vast  number  and  diversity 
of  nations  which  it  embraces,  necessitates,  in  a  much 
greater  degree,  the  fixing  of  a  good  outline  in  the  mind 
of  the  /pupil,  as  preliminary  to  a  more  minute  study  of 
the  subject. 


HISTORY.  239 

This  outline  should  be  brief,  but  should  show  clearly 
the  chronological  and  geographical  relations  of  the  na- 
tions, the  history  of  which  is  to  be  studied,  and,  to 
some  extent,  their  ethnological  relations.  When  this 
has  been  done,  it  will  be  perfectly  easy  to  take  up  the 
history  of  any  nation  comprehended  in  the  outline,  and 
to  treat  it  intelligibly. 

The  use  of  maps,  charts,  and  synchronous  tables,  will 
aid  very  much  in  impressing  firmly  upon  the  pupil's 
mind  such  an  outline  as  is  here  suggested.  The  maps 
used  should  show  clearly  and  accurately  the  territorial 
extent  and  relations  of  the  various  nations  generally 
treated  of  in  ancient,  mediaeval,  and  modern  history. 
All  names  of  places  referred  to  should  be  carefully 
pointed  out  on  the  map,  so  that  their  exact  location 
may  be  constantly  kept  in  view.  This  will  aid  the 
memory  very  much,  as  it  brings  into  play  the  faculty  of 
conception. 

In  the  arrangement  of  topics  the  order  of  time  should 
be  carefully  followed  at  first,  and  the  date  (year)  of 
each  important  event  kept  before  the  mind  of  the  pupil. 
A  few  leading  dates  should  be  carefully  memorized. 
After  the  history  of  different  nations  has  been  studied, 
the  leading  events  of  each  should  be  arranged  in  syn- 
chronous tables.  The  reigns  of  contemporaneous  sove- 
reigns, for  example,  should  be  compared,  and  the  con- 
nection of  events  in  each  carefully  studied. 

Reviews,  such  as  are  suggested  in  connection  with 
the  United  States  history,  by  a  chronological,  geographi- 
cal, and  biographical  arrangement  of  topics,  should  be 
given  with  sufficient  frequency. 

The  following  syllabus  presents  the  topics  which 
should  be  embraced  in  the  outline  above  suggested : 


240  HOW  TO  TEACH 

SYLLABUS  OF  TOPICS. 

1.  The  nations  and  countries  of  the  most  remote  antiquity — 
Egypt  and  Ethiopia,  Babylonia  and  Assyria,  Lydia,  Media,  Syria 
und.  Palestine,  Persia.   Of  these  only  a  brief  sketch  need  be  learned. 

2.  GREECE — the   mythologic   period  (very  brief) ;  the  period 
from  the  beginning  of  the  Persian  war  to  the  Roman  conquest  of 
Greece.    This  will  include  the  rise  and  fall  of  the  Macedonian 
Empire,  with  its  divisions  under  Alexander's  successors. 

3.  ROME — the  legendary   period  ;  the   foundation  of  the  Re- 
public in  its  various  stages,  including  the  contests  between  the 
orders  of  Patricians  and  Plebeians  ;   the  successive  wars  with  the 
Samnites,  Carthaginians,  etc. ;  the  civil  wars,  including  the  trium- 
virates ;  the  fall  of  the  Republic,  and  the  foundation  of  the  Em- 
pire under  Augustus.    Tlie  territorial  conquests  should  be  shown 
in  connection  with  this. 

4.  THE  ROMAN  EMPIRE— its  territorial  acquisitions  and  chan- 
ges from  Augustus  to  the  division  of  the  Empire  at  the  death  of 
Theodosius,  including  a  brief  sketch  of  the  principal  reigning 
emperors,  and  the  invasions    by  the  Goths,  Huns,  and  Vandals. 

o.  THE  WESTERN  EMPIRE,  from  Houorius  to  its  fall  under 
Augustuius  (brief),  including  the  barbaric  invasions. 

6.  THE  EASTERN  EMPIRE — from  Arcadius  to  the  taking  of 
Constantinople  by  the  Ottomans  ;  a  brief  sketch,  including  the 
wars  with  the  Goths,  Saracens,  Seljuks,  Mongols,  and  Ottomans. 

7.  THE  SARACENIC  EMPIRE — a  brief  sketch  of  its  foundation, 
its  territorial  conquests  and  extent,  its  divisions,  and  its  fall. 

8.  FRANCE — the  invasion  of  Gaul  by  the  Franks,  and  founda- 
tion of  the  Merovingian  Dynasty  ;  a  brief  sketch  of  it ;  the  Car- 
lovingian  Dynasty,  including  Charlemagne's  conquests,  and  the 
revival  of  the  Western  Empire  ;  the  Capetian  Dynasty  to  the  end 
of  the  Reign  of  Louis  XL     This  will  include  the  Crusades. 

9.  ENGLAND— a  brief  sketch    of  British    History  before   the 
time  of  Egbert ;  from  Egbert  to  the  Tudors.     (England  maybe 
studied  first,  if  it  is  preferred.) 

10.  Other  nations  contemporaneous  with  England  and  France. 
(Very  briefly.) 

11.  MODERN    HISTORY — in  a  similar  manner;   England  and 
France,  as  the  leading  nations;  other  nations,  including  Ger- 
many, Prussia,  Russia,  etc. 


ELEMENTARY  SCIENCE.  241 

12.  AMERICAN  HISTORY — not  immediately  connected  with 
U.  S.  History. 

Other  parts  of  the  world  as  China,  India,  etc.,  may  be  omitted 
in  this  preliminary  outline — which  is  all  that  can  generally  be 
pursued  in  the  Common  Schools. 

This  history  should  be  so  studied  as  to  induce  the 
pupils  to  read  standard  writers  upon  the  most  impor- 
tant topics.  The  instruction  should  embrace  advice 
and  direction  as  to  the  best  writers  in  each  period  and 
nation.  Historical  selections  will  be  found  valuable  for 
this  purpose. 


ELEMENTARY  SCIENCE 

(BY  ORAL  INSTRUCTION  OR  A  SIMPLE  TEXT-BOOK.) 

Natural  Philosophy. — For  general  suggestions, 
see  preceding  grade. 

SYLLABUS  OF  TOPICS. 

Acoustics.— Preliminary — a  general  idea  of  the  transmission 
of  vibrations  illustrated— tlie  nature  of  sound — sounding  bod- 
ies— a  medium  necessary — the  air  as  a  medium — other  media — 
limits  of  audibility  of  vibrations — velocity  in  air  and  other 
media — loudness  does  not  alter  the  velocity — reflection  of 
sound — echo,  its  causes  and  limits — physical  distinction  of 
noise  from  music — pitch  in  music — effects  of  tension  upon 
vibrating  wires — influence  of  sound  boards— tuning-forks — 
speaking-trumpets,  speaking-tubes  —  resonance  —  murmur  of 
shell  —  the  ear,  its  construction  and  action — the  wonderful 
physical  condition  of  the  tympanum  when  listening  to  a  full 
orchestra. 

Pyronomics. — Heat — known  only  by  its  effects — effect  on  the 
nerves — effect  upon  the  constitution  of  bodies — transmission 
of  heat — the  three  methods  of  transmission  illustrated — air  a 
bad  conductor  nnd  worse  rarlia'or — important  relation  of  this 
fact  to  clo'liing,  to  vegetation,  etc. — ln-at  as  a  sensation — icla- 
11 


242  HOW  TO  TEACH 

tion  of  terms  hot  and  cold — sources  of  heat — quantity  and  effects 
of  solar  heat — its  relations  to  physical  geography  —  source 
of  the  heat  developed  by  friction — motion  of  mass  converted 
into  molecular  motion — heat  only  a  mode  of  vibratory  motion 
— force  as  indestructible  as  matter — source  of  heat  in  combus- 
tion— the  thermometer — principles  employed  in  its  construc- 
tion— nature  and  determination  of  the  zero — evaporation — its 
causes — effects  on  temperature  of  bodies — phenomena  of  boil- 
ing— temperature  of  boiling  water — why  invariable  at  a  given 
elevation— economic  applications — why  the  boiling  point  varies 
with  elevation — boiling  in  a  closed  vessel — the  steam  engine — 
its  essential  elements  and  general  principles — high-pressure  and 
low-pressure  engines. 

Optics. — Light — moves  in  straight  lines  —  shadows  —  sources 
of  light — vibratory  nature  of  light  (only  refer  to  it) — velocity 
of  light — how  known — law  of  intensity  illustrated — photome- 
try by  shadows — non-luminous  bodies — how  seen — reflection — 
its  law — mirrors,  and  their  uses  (treat  more  fully  of  the  plane 
mirror  than  of  the  others) — refraction — its  simplest  phenomena 
— its  law — lenses — uses  of,  especially  the  convex  lens — color 
— the  prism  and  the  solar  spectrum — the  order  of  the  colors 
(refer  very  briefly  to  thermic  and  actinic  rays) — Frauenhofer's 
lines  (brief) — phenomena  of  the  rainbow — the  colors  of  objects 
— primary  colors — the  eye  and  vision. 

Magnetism. — Magnets,  natural  and  artificial — forms  of  artifi- 
cial magnets — polarity — attraction  and  repulsion — magnetic  in- 
duction— temporary  and  permanent  magnets — the  Earth  a  mag- 
net— magnetic  needle,  and  why  it  points  to  the  north. 

Electricity. — Frictional  electricity — conductors  and  non-con- 
ductors— electricity  not  a  fluid  but  a  polarizing  force,  related 
to  magnetism — attraction  and  repulsion — electric  induction — in- 
sulators— effects  of  points — atmospheric  electricity — its  origin — 
lightning-rods — the  flash — the  white  hot  air — the  thunder — pop- 
ular fallacies  as  to  electric  fluids,  thunder-bolts,  heat-lightning, 
and  the  cause  of  thunder  —  current  electricity  from  chemical 
action — a  battery,  its  wires  and  poles — polarized  condition  of  the 
parts — how  to  develop  heat  and  light — uses  made  of  those — sim- 
ple helix — simple  galvanometer — magnetism  developed  by  elec- 
tric current — temporary  magnet  and  magnetic  telegraph. 


ASTRONOMY.  243 

Astronomy. — The  topics  embraced  in  the  preced- 
ing grade  should  be  carefully  reviewed  in  this  grade,  as 
far  as  may  be  necessary  to  secure  thorough  preparation 
for  the  advanced  portions  of  the  subject,  which  consti- 
tute the  special  work  of  the  grade.  The  use  of  the 
globes  should  be  continued,  in  order  more  fully  to  fa- 
miliarize the  pupils  with  the  Doctrine  of  the  Sphere — so 
important  to  a  clear  understanding  of  astronomical  facts. 

The  interest  of  the  pupils  in  the  observation  of  astro- 
nomical phenomena  should  be  sustained  by  calling  their 
attention  as  frequently  as  possible  to  facts  which  they 
can  verify  in  this  way.  By  degrees,  the  pupils  should 
be  induced  to  familiarize  themselves  with  the  locations, 
at  different  seasons  of  the  year,  at  a  given  time  by  the 
clock,  of  the  most  conspicuous  constellations  and  stars. 
The  use  of  the  Celestial  Globe,  or  a  planisphere,  will 
furnish  valuable  aid  in  the  accomplishment  of  this. 
The  positions  of  the  planets  Jupiter,  Saturn,  Mars, 
Venus,  and  Mercury,  among  the  stars,  should  be»kept 
constantly  in  view,  together  with  their  apparent  mo- 
tions, and  general  progress  eastward.  The  use  of  a 
good  almanac  will  afford  assistance  in  accomplishing 
what  is  here  suggested ;  also  in  calling  attention  to 
the  more  unusual  phenomena  connected  with  eclipses. 

The  folloAving  topics  should  be  specially  treated  in 
this  grade : 

SYLLABUS  OF  TOPICS. 

1.  THE  SUN — its  magnitude,  real  and  apparent ;  distance  from 
the  earth  (give  a  general  idea  of  the  manner  of  finding  this,  al- 
though a  minute  knowledge  of  parallax  may  be  reserved  for  the 
more  advanced  part  of  the  subject);    solar  spots— theory  with 
regard  to  their  cause,  their  apparent  motions,  what  is  deduced 
from  this.  The  Zodiacal  light  maybe  briefly  referred  to  in  connec- 
tion with  the  Sun. 

2.  THE  PRIMARY  PLANETS — in  succession,  commencing  with 


244  HOW  TO  TEACH 

Mercury,  the  pupil  to  learn  the  most  important  facts  in  relation 
to  their  orbits,  magnitudes,  telescopic  appearance,  synodic  and 
sidereal  periods,  axial  rotations,  apparent  motions,  seasons, 
satellites,  etc.  The  Asteroids,  their  orbits,  etc.  Any  interesting 
facts  in  relation  to  the  history  of  astronomical  discovery  should 
be  communicated  incidentally,  as  this  will  serve  to  make  the 
subject  more  attractive. 

3.  THE  MOON — in  a  similar  manner,  teaching  about  its  phases 
and  their  cause,  its  revolutions,  periods,  Harvest  Moon,  Librations, 
and  a  brief  general  description  of  the  lunar  surface  (Selenog- 
raphy). 

4.  ECLIPSES — solar  and  lunar  ;  total  and  partial,  how  caused  ; 
comparative  frequency — ecliptic  limits.     Transits,  their  cause — 
why  important. 

5.  TIDES — flood  and  ebb,  spring  and  neap,  how  caused  ;  prin- 
cipal facts  connected  with  them  ;  the  tidal  wave  ;  height  of  tide 
at  different  places — primitive  and  derivative  tides. 

6.  COMETS — their  peculiar  appearance,  the  different  parts  of 
which  they  are  composed  ;  different  kinds  of  comets  ;  periodic 
times  of  the  comets  of  short  period — interesting  facts  iu  relation 
to  the  orbits,  size,  mass,  density,  and  apparent  magnitude  of  con- 
spicucjus  comets. 

7.  A  brief  account  of  Meteors,  their  supposed  nature  and  origin 
--cause  of  the  periodic  displays  of  meteors. 

8.  STARS — classification — the  constellations — names,  classifica- 
tion of,  brightest  stars  in  each — apparent  change  in  position  due 
to  precession  ;  cause  of  precession  ;  exercises  in  finding  the  con- 
stellations visible  at  anytime  ;  the  galaxy  ;  proper  motion  of  the 
stars;  multiple  stars  ;  variable  and  temporary  stars;  distances  of 
stars,  how  found;  parallax,  diurnal  and  annual. 

9.  NEBULA — classification   of;  their  nature  and  appearance; 
general  location  and  appearance  ;  the  location  andappearance  of 
the  most  noted. 

10.  TIME — how  measured  ;  solar,  sidereal,  and  civil  day  ;  why 
the  solar  exceeds  the  sidereal  day  ;  why  the  solar  days  are  un- 
equal ;  equation  of  time  ;  tropical,  sidereal,  and  civil  years,  how 
and  why  they  differ  in  length. 

11.  ASTRONOMICAL  REFRACTION— its  effect  upon  the  apparent 
positions  of  the  heavenly  bodies  ;  variation  at  different  altitudes. 

12.  GENERAL  UKVIEW. 


CHEMISTRY.  245 

In  giving  instruction  in  this  subject,  its  special  office 
as  a  means  of  training  the  concept  ivc  faculty,  should  be 
kept  steadily  in  view.  Facts  of  observation  and  facts  of 
inference  should  be  carefully  distinguished.  Apparatus 
and  diagrams  will  afford  some  aid  in  enabling  the  mind 
to  grasp  the  more  difficult  facts  of  inference  ;  but  the 
actual  observation  of  the  phenomena  to  be  illustrated 
should  precede,  as  far  as  possible,  the  use  of  these. 
Thus,  a  good  tellurian  will  illustrate  clearly  the  causes 
of  the  change  of  the  seasons,  and  a  diagram  may  be 
made  to  show  the  reason  of  their  unequal  duration;  but 
the  facts  of  these  changes  and  inequalities  must  first  be 
clearly  apprehended  by  the  mind.  If  this  is  done,  the 
natural  curiosity  to  know  the  cause  will  make  the  pupils 
more  attentive  to  the  instruction  given.  Cumbrous 
and  complicated  machinery,  without  the  attentive  ob- 
servation of  the  natural  phenomena,  and  the  conceptions 
based  upon  them,  rather  serve  to  give  false  notions  than 
to  impart  clear  ideas  of  the  actual  facts.  A  good  plani- 
sphere will  prove  a  valuable  aid  in  the  study  of  uranog- 
raphy. 

Nor  should  the  teacher  fail,  in  connection  with  the 
instruction,  incidentally  to  impress  upon  the  pupil's 
mind  that,  in  studying  the  laws  of  the  universe,  he  is 
contemplating  the  works  of  a  beneficent  Creator,  infi- 
nite in  wisdom  and  power.  No  subject  is  so  well  quali- 
fied as  astronomy  to  give  just  ideas  in  this  respect,  and, 
while  performing  a  peculiar  and  most  important  office 
in  the  training  and  development  of  the  intellectual  pow- 
ers, to  exalt  the  understanding  and  give  elevation  and 
tone  to  the  whole  character. 

Chemistry.— The  instruction  given  in  chemistry 
in  the  common  schools,  like  that  given  in  physics  and 


24G  JIOW  TO  TEACH 

in  the  natural  sciences,  must  necessarily  be  at  the  most 
only  rudimental.  Whole  sections  of  each  subject  must 
be  omitted.  In  every  department  of  oral  instruction  in 
science,  the  principal  object  should  be  to  form  the  mind 
to  proper  habits  of  observation.  This,  together  with 
the  knowledge  of  the  facts  and  principles  of  science 
incidentally  thus  imparted,  is  a  preparation  for  the 
systematic  study  of  these  sciences,  rather  than  a  formal 
attempt  to  impart  a  knowledge  of  their  complete  out- 
lines. Yet  this  knowledge  of  the  facts  and  principles 
thus  obtained,  is  in  itself  of  so  great  practical  import- 
ance as  to  render  it  an  indispensable  part  of  any  proper 
scheme  of  common  school  education. 

The  process  employed  should,  as  far  as  practicable, 
be  the  same  as  that  suggested  for  the  instruction  in 
natural  philosophy.  The  lesson,  when  not  a  review, 
should  usually  begin  with  an  experiment.  The  facts 
to  which  the  attention  of  the  pupils  is  particularly 
directed,  should,  as  far  as  possible,  relate  to  the  chemis- 
try of  common  things  or  of  every-day  life.  They  should 
be  so  taught  as  to  leave  in  the  mind  of  the  pupil  a 
determination  and  a  conscious  ability  to  know  more  of 
a  science  so  highly  practical,  so  intensely  interesting, 
and  so  obviously  within  his  own  power  to  acquire. 

As  in  Natural  Philosophy,  the  greater  part,  or 
even  the  whole,  of  the  necessary  apparatus  may,  with 
a  little  ingenuity,  be  extemporized.  As  a  stimulus  to 
the  inventive  powers  of  the  pupils,  this  is  in  itself  an 
important  matter  in  practical  training,  and  will,  per- 
haps more  than  anything  else,  insure  the  further  prose- 
cution of  the  subject  by  the  pupils  themselves.  There 
are  so  many  excellent  text-books  in  the  rudiments  of 
this  science,  all  abounding  with  practical  hints  and 
illustrations,  in  relation  to  the  construction  of  such 


CHEMISTRY.  047 

apparatus,  that  it  is  not  necessary  here  to  do  more  than 
refer  to  them. 

.  The  following  syllabus  of  topics,  together  with  a  few 
experimental  illustrations  therein  introduced,  is  chiefly 
intended  to  show  how  the  objective  process  of  instruc- 
tion may  be  applied  to  the  study  of  facts  in  chemistry, 
the  subject  being  quite  as  profitably  and  easily  approach- 
ed from  any  one  of  a  dozen  starting-points,  other  than 
the  one  here  selected.  No  other  department  of  science 
can  be  made  to  show  the  value  of  this  process  more 
clearly,  or  to  furnish  more  important  mental  discipline. 
Experiment  must  be  made  to  raise  questions  in  the 
mind  of  the  pupil,  only  to  be  answered  by  deductions 
from  further  experiment. 

A  small  portion  only  of  the  subject  can  here  be  suffi- 
ciently expanded  to  illustrate  the  process,  the  further 
details  being  necessarily  left  to  the  ingenuity  of  the 
teacher. 

SYLLABUS  OP  TOPICS. 

FORCES. — (Begin  with  a  very  brief  review  of  the  following 
points  in  Natural  Philosophy.)  All  changes  in  matter  are 
effected  by  forces;  examples  of  physical  changes  wrought  by 
physical  forces,  in  pulverizing,  solution,  fusion,  polarization,  etc., 
in  which  the  substance  remains  unchanged  in  composition  and 
general  properties. 

CJiemiad  changes  ;  those  in  which  the  substance  has  changed 
its  properties ;  experimental  illustrations :  (use  no  chemical 
names  or  terms  at  this  srage  of  the  work ;  use  well-known  com- 
mon names  as  far  as  possible  at  first,  such  as  sulphur,  copper, 
blue  vitriol,  alcohol,  etc.) 

Exp.  1st.  Show  copper  filings  and  pulverized  sulphur ;  let  the 
properties  of  each  be  objectively  noted;  melt  them  together 
slowly  ;  notice  the  heat  given  out  in  the  process  ;  examine  the 
substance  produced  by  the  combination  ;  it  is  neither  copper 
nor  sulphur ;  compare  with  a  similar  mixture  of  melted  sugar 
and  sand  ;  solution  will  show  these  last  unchanged. 


248  HOW  TO  TEACH 

Exp.  2d.  Burn  sulphur  iu  air ;  the  sulphur  disappears,  and  an 
invisible  sour  gas  is  formed,  perceived  by  the  lungs  and  the 
smell ;  has  been  made  from  the  sulphur  and  the  air. 

Exp.  3d.  Burn  alcohol  or  kerosene  in  air:  show  water  as  a 
product;  heat  given  out  in  all  these  changes  of  substance.  - 

Chemical  attraction :  such  changes  are  produced  by  a  force 
known  as  chemical  attraction  or  chemical  affinity  :  the  atoms  of 
sulphur  and  copper  attracted  each  other  and  formed  a  new  sub- 
stance ;  (omit  its  name) ;  this  force  frequently  breaks  old  combi- 
nations to  form  new  and  stronger  ones. 

Exp.  £th.  Make  a  solution  of  blue  vitriol  (copper  sulphate),  in 
a  small  vial,  dip  a  clean  knife-blade  into  it;  copper  is  deposited 
on  the  blade  ;  ask  what  substance  must  have  been  contained  in 
the  transparent  blue  vitriol ;  tell  that  this  copper  was  combined 
with  another  substance  which  has  taken  up  some  of  the  iron, 
at  the  same  time  rejecting  or  throwing  down  a  part  of  the 
copper. 

Elements  (nearly  all  to  be  told)  ;  iron  and  sulphur  called 
elements  ;  why  ;  there  are  many  elements  (G5) ;  some,  like  iron 
and  copper  are  metals  ;  therefore  called  metallic  elements  ;  all  the 
rest,  like  sulphur,  are  called  non-metallic  elements;  about  a 
dozen  elements  compose  the  greater  part  of  the  material  of  all 
known  substances  ;  nearly  every  substance,  water,  rocks,  plants, 
and  animals  consists  of  chemical  compounds. 

Carbonic  acid  (carbonic  dioxide  ;  carbonic  anhydride;  use  none 
of  the  names  at  first).  What  is  it  that  bubbles  in  soda-water? 
How  do  you  know  that  it  is  not  air  ?  Its  taste  ;  its  smell ;  why 
called  acid  (reserve  the  scientific  definition  of  an  acid). 

Exp.  5th.  Show  marble  fragments,  or  chalk  (not  the  plaster 
cylinders  used  upon  the  blackboard).  Show  muriatic  acid ; 
dilute  a  little  with  water  ;  taste  it ;  an  acid ;  pour  the  dilute 
acid  upon  the  marble  or  chalk.  (A  small  bottle,  bent  tube,  and 
receiving-bottle  for  the  gas  are  necessary.)  Smell  the  gas  ;  com- 
pare changes  which  have  taken  place  with  those  of  copper  and 
the  iron  in  Exp.  4;  one  acid  has  taken  the  place  of  the  other; 
the  acid  gas  must  have  been  solid ;  the  force  which  held  it  so 
compressed. 

Exp.  Qt?t.  Burn  a  piece  of  marble  or  chalk  in  a  charcoal  fire ; 
lime  kilns  ;  marble  changed  to  lime ;  properties  different ;  tell 
that  the  great  heat  has  driven  off  the  gas. 


CHEMISTRY.  249 

Exp.  1th.  Make  and  filter  lime-water ;  agitate  some  of  the  gas 
of  Exp.  5  with  lime-water  in  a  bottle ;  water  becomes  milky ; 
the  gas  has  united  with  the  lime  as  before  burning ;  chalky 
sediment  settles  ;  lime  water  a  test  for  this  gas  ;  meaning  of  the 
term  test. 

Exp.  8th.  Agitate  the  gas  from  soda-water  with  lime-water: 
result  identical  with  the  last ;  therefore  the  gas  in  soda-water  is 
the  same  as  that  from  the  marble. 

Exp.  Qth.  Burn  a  candle  in  an  open  wide-mouthed  jar  ;  close 
the  jar  tightly;  candle  soon  goes  out;  a  part  of  the  candle  has 
disappeared  ;  test,  as  before,  the  air  that  is  left  in  the  jar ;  there- 
fore the  same  gas. 

Exp.  Wth.  Let  the  burning  caudle  smoke  or  smut  white 
paper ;  tell  and  show  that  the  smut  or  lamp-black  is  charcoal ; 
its  better  name,  carbon. 

Exp.  \Wi.  Burn  ordinary  charcoal;  it  seems  to  have  dissolved 
in  the  air ;  gather  the  air  from  it ;  test  it ;  now  use  the  popular 
name,  carbonic  acid  gas  (other  and  better  names  to  be  learned 
hereafter) ;  therefore  carbon  in  the  candle;  in  kerosene;  in  all 
fats,  coal,  bread,  wood,  etc.  Show  by  over-baked  bread,  meat, 
by  wood,  etc. 

Exp.  12th.  Blow  breath  through  a  straw  or  a  pipe  stem  into 
lime-water ;  test  shows  abundant  carbonic  acid ;  from  bread, 
vegetables,  and  other  food. 

Exp.  \Wi.  Collect  from  marble  a  quantity  of  the  gas ;  show 
that  it  will  not  support  combustion  ;  fatal  to  life  ;  the  gas  in 
mines,  wells,  vats,  etc.;  suicide  with  charcoal;  necessity  of 
thorough  ventilation. 

In  the  same  manner  oxygen  may  now  be  considered,  its 
properties  and  functions  shown,  and  its  principal  compounds, 
including  the  carbonic  acid  of  the  preceding  experiments.  Hy- 
drogen, chlorine,  and  nitrogen  may  be  next  in  order. 

REVIEW.  At  this  stage  it  is  desirable  to  review,  rearrange,  and 
explain  the  knowledge  already  acquired,  under  the  following 
heads  : 

Chemistry  of  water :  hydrogen,  oxygen;  solution  of  solids  and 
gases  in  water  ;  hard  and  soft  waters  ;  mineral  waters. 

Chemistry  of  tlie  atmosphere  :  combustion  ;  nitrogen  ;  carbonic 
acid  ;  its  relations  to  plants  and  to  animals ;  illuminating  gas. 

Chemistry  of  rocks  and  soils:  limestone  and  lime;  quartz, 
11* 


250  HOW  TO  TEACH 

sandstones,  and  silica ;  clay,  slate,  and  alumina  ;  granite,  feld- 
spar, potash,  soda,  etc. ;  common  salt. 

Chemistry  of  plants  and  animals :  starch,  gum,  sugar,  lignin, 
vegetable  and  animal  oils,  albumen,  gluten,  etc. 

Special  topics :  bread-making,  soap-making,  glass-making,  fer- 
mentation, distillation,  photography,  etc.,  etc. 


MISCELLANEOUS  BRANCHES. 

Book  -  keeping. — After  the  forms  required  in 
single-entry  book-keeping  have  been  taught,  which 
should  be  quite  brief,  the  nature  of  double-entry  book- 
keeping should  be  explained,  by  showing  the  relation  of 
debit  and  credit,  and  how  the  former  in  one  account 
may  be  exactly  balanced  in  another,  so  that  one  set  of 
entries  may  be  made  to  verify  the  accuracy  of  another, 
and  thus  prevent  the  admission  of  any  errors  Avhich 
may  not  be  readily  discovered  and  rectified. 

2.  The  classification  of  accounts  should  be  followed 
by  an  explanation  of  the  three  books — Day-book,  Jour- 
nal, and  Ledger.     Journalizing  simple   entries  in  the 
Day-book  should  then  be  taught;  and  sufficient  exer- 
cises given  to  impart  readiness  and  accuracy  in  the  pro- 
cess.    The  keeping  of  a  simple  and  brief  set  of  accounts 
will  then  render  the  whole  process  and  theory  intelli- 
gible to  the  pupils'  minds,  and  will  also  render  them 
sufficiently  expert  in  their  application. 

3.  All  the  common  business  forms  should  be  taught ; 
as  the  form  of  bills,  receipts,  bank  checks,  promissory 
notes,  bills  of  exchange,  invoices,  etc.,  etc.     Business 
correspondence  should  also  receive  some  attention.     Ifc 
is  of  great  importance  to  render  the  pupils  expert  in 
writing    a    good    business    letter.      In    every   exercise 
fluency,  legibility,  and  grace  in  penmanship  should  be 


MISCELLANEOUS  BRANCHES.  251 

carefully  attended  to.  Quantity  and  quality  should  both 
be  insisted  on  in  this  respect. 

Constitution  of  the    United  States. — The 

recommendation  to  teach  the  Constitution  of  the  United 
States  applies  to  pupils  of  both  sexes  in  this  grade.  It 
would  appear  to  be  essential  that  those  who  pass 
through  a  full  course  for  common  schools  should  have 
some  knowledge  of  the  simple  principles  and  require- 
ments of  the  organic  law  of  the  nation — the  distri- 
bution of  the  powers  of  the  general  government,  and 
the  rights,  duties,  and  obligations  of  an  American 
citizen. 

The  Constitution  itself  should  be  the  text  studied, 
the  pupils  being  made  familiar,  as  far  as  possible,  with 
the  language  of  tbe  instrument,  and  also  instructed  in 
the  meaning  and  intention  of  the  several  provisions. 
Several  matters,  purely  technical,  will  need  to  be  care- 
fully elucidated,  such  as  ex-post-facto  laws,  Mlh  of  at- 
tainder, habeas  corpus,  etc.,  etc.  The  history,  English 
and  American,  particularly  the  former,  with  which 
these  are  connected,  will  prove  a  most  instructive  and 
interesting  subject  for  comment  by  the  teacher. 

Questions  as  to  the  construction  of  certain  points  in 
the  Constitution,  which  have  been  in  agitation  at  vari- 
ous times,  during  the  past  history  of  the  country,  would 
prove,  in  boys'  classes  especially,  as  far  as  time  and  op- 
portunity may  admit,  very  beneficial  for  discussion,  as 
tending  to  impart  readiness  in  speech,  as  well  as  self- 
reliance  and  freedom  in  thought  and  opinion. 


252  HOW  TO  TEACH. 


GENERAL   SUGGESTIONS 

RELATIVE  TO  THE  CLASSIFICATION  AND  INSTRUCTION 
OF  PUPILS  IN  SCHOOLS. 

Reviews. — Such  a  review  of  previous  lessons,  in 
connection  with  each  new  lesson  on  the  same  subject, 
should  be  ftiven  as  will  cause  the  pupils  properly  to  asso- 
ciate together  the  facts  learned  in  all  of  them,  and  thus 
lead  them  to  acquire  a  comprehensive  as  well  as  a  famil- 
iar knowledge  of  each  subject  contained  in  the  grade  or 
the  course. 

General  reviews  of  subjects  should  be  had  at  least  as 
often  as  once  during  each  month ;  and  in  these  the  lead- 
ing facts  learned  in  previous  grades  should  be  included. 

Progress  of  Classes. — Whenever  it  is  found  that  a 
class  has  advanced  further  in  one  or  more  subjects  of  its 
grade  than  it  has  in  others,  less  time  should  be  devoted 
to  these  subjects,  and  more  to  others,  so  that  the  grade 
of  the  class  may  be  equalized  in  all  its  studies.  No 
study  of  a  succeeding  grade  should  be  introduced  into 
a  class  of  a  lower  grade  until  the  class  has  completed  the 
requirements  of  the  grade  in  all  the  branches  of  study 
included  therein. 

Progress  of  Pupils. — It  often  happens  that  a 
few  of  the  pupils  of  a  class  will  so  far  outstrip  their  fel- 
lows in  a  single  month,  as  to  render  it  necessary  to  trans- 
fer these  rapid  learners  to  a  class  of  the  next  higher 
grade.  While  great  care  should  be  exercised  not  to  stimu- 
late the  excessive  mental  activity  or  precocity  of  young 
pupils,  yet  the  disparity  of  progress  in  pupils  of  the 
same  class  may  sometimes  be  used  as  an  incentive  to 


GENERAL  SUGGESTIONS.  353 

urge  forward  those  who  are  extremely  sluggish  or  inert. 
This  may  be  done  by  promoting  in  a  public  manner,  at 
the  end  of  each  month,  two  or  three  of  the  pupils  who 
are  found  to  have  made  the  greatest  improvement,  into  a 
higher  class  of  the  same  grade.  In  doing  this,  however, 
care  must  be  taken  not  to  disturb  the  gradation  by  per- 
mitting pupils  to  omit  important  branches  of  study.  As 
a  general  thing  every  pupil  should  be  required  to  spend 
the  whole  time  which  may  be  prescribed  for  the  grade. 

Recitations. — No  class  in  the  primary  grades 
should  be  required  to  spend  more  than  half  an  hour, 
at  one  time,  in  the  same  exercise.  The  mind,  as  well 
as  the  body,  needs  rest.  A  change  of  subject,  and  a 
change  in  the  manner  of  conducting  class  exei'cisps, 
are  both  necessary  in  order  to  furnish  opportunities  for 
rest  during  school  hours. 

The  recitations  should  be  spirited  exercises.  The 
questions  should  be  as  definite  as  possible.  The  teacher 
should  carefully  avoid  implying  in  the  question  any  of 
the  facts  or  principles  that  should  be  stated  directly  by 
the  pupil.  The  habit  of  repeating  the  pupil's  answer 
should  also  be  avoided.  Pupils  should  be  invariably 
required  to  use  natural  and  proper  tones  in  recitation, 
to  emmciate  distinctly,  and  to  avoid  grammatical  errors. 
If  this  be  not  done,  the  lessons  in  reading  and  grammar 
will  be  of  little  avail  to  break  up  pernicious  habits  of 
speech,  which  the  teacher,  by  his  neglect,  will  have  as- 
sisted to  fix. 

Unless  thoroughly  familiar  with  the  details  of  the 
text-book,  the  teacher  needs  special  and  renewed  prep- 
aration quite  as  much  as  the  pupils.  Without  this, 
he  will  not  succeed.  In  hearing  the  recitations,  he 
should  carefully  discriminate  between  the  statements 


254  JWW  TO  TEACH. 

found  in  the  text-book  and  additional  ones  which  he 
may  have  found  necessary  to  make  in  the  preparatory 
explanation  of  the  lesson,  and  which  the  pupil  may  have 
had  no  opportunity  to  con  over. 

Lessons  for  Home  Study. — In  every  class,  how- 
ever well  graded,  the  pupils  will  differ  much  in  age, 
health,  mental  capacity,  and  home  advantages.  A  cor- 
rect and  judicious  classification  will  reduce  this  inequal- 
ity to  a  minimum;  but  there  will  still  remain  a  wide 
field  for  the  exercise  of  discrimination,  care,  and  caution 
on  the  part  of  the  class  teacher.  The  lessons  should,  in 
all  respects, be  adapted  to  the  average  ability  of  the  pupils 
of  the  class;  but,  even  beyond  this,  some  allowance  will 
often  have  to  be  made  in  the  case  of  pupils  of  quite  in- 
ferior mental  capacity  or  opportunities  for  home  study. 
Teachers  must  bear  in  mind  that  the  one  great  object 
of  home  study  is  to  train  the  pupils  to  self-exertion, — 
to  give  them  the  ability  to  depend  upon  their  own 
efforts  as  students,  and  by  degrees,  to  dispense  with  the 
aid  of  a  teacher.  It  is,  therefore,  of  supreme  impor- 
tance to  avoid  everything  that  would  discourage,  or  de- 
prive of  self-reliance;  and  nothing  has  a  stronger  ten- 
dency in  this  direction  than  the  imposition  of  excessive 
tasks. 

Teachers  are  especially  admonished  to  be  considerate 
toward  pupils  of  a  delicate  constitution,  an  over-excita- 
ble brain  and  nervous  system,  or  in  temporary  ill-health. 
Many  children  of  this  class  are  precocious  in  mental 
activity  and  exceedingly  ambitious  to  excel;  and  the 
greatest  care  is  required  to  prevent  them  from  injuring 
themselves  by  an  inordinate  devotion  to  books  and 
study. 

The  length  of  the  tasks  imposed  should,  therefore,  be 


GENERAL  Sl'GGESHOXS.  055 

most  carefully  scrutinized  and  adjusted.  The  practice 
of  assigning  a  fixed  number  of  words,  lines,  paragraphs, 
pages,  or  examples,  without  a  minute  inspection  of  their 
nature  or  contents,  is  often  accompanied  with  disastrous 
results.  The  pupils  are  wearied  and  discouraged;  and 
the  parents,  finding  the  work  of  the  school-room  trans- 
ferred to  the  home  circle,  lose  all  confidence  in  the 
judgment  and  ability  of  the  teacher. 

The  teacher  should  ascertain,  the  methods  which 
pupils  employ  in  home-study.  Verbatim  study,  except- 
ing in  case  of  important  definitions,  is  to  be  discouraged. 
While  making  the  necessary  preliminary  explanations, 
a  brief  abstract  of  the  leading  points  should  be  written 
upon  the  blackboard,  and  made  the  basis  of  the  recita- 
tion. This  will  do  much  to  induce  a  rational  method 
in  study,  and  prevent  a  slavish  adherence  to  the  text. 

The  teacher  should  advise  Avith  his  pupils  as  to  their 
time  and  opportunities  for  home  study.  Household 
duties,  cramped  and  noisy  homes,  and  deficient  light, 
no  doubt  greatly  obstruct,  in  many  cases,  the  pupils' 
efforts.  These  should  be,  as  far  as  possible,  ascertained 
and  allowed  for.  Very  small  print  should  be  entirely 
excluded  from  home  lessons  on  account  of  its  tendency 
to  produce  myopy,  when  studied  by  artificial  light. 
Many  hours  of  confinement  in  a  crowded  class-room, 
with  the  long-continued  and  close  attention  required 
there,  renders  rest  and  relaxation,  with  some  kind  of 
physical  exercise,  indispensable  to  growing  boys  and 
girls.  The  teacher  should,  at  least,  advise  that  these 
come  before  home-study. 

Physical  Training. — The  pupils  should  be  ex- 
ercised, as  much  as  may  be  practicable,  in  such  a  way 
as  to  expand  the  lungs,  develop  the  muscular  system, 


256  SOW  TO  TEACH. 

and  impart  an  easy  and  graceful  carriage  to  the  body. 
In  schools  for  boys,  the  marching  drill  should  be  em- 
ployed in  the  ordinary  evolutions  of  the  schools,  with 
such  instruction  as  may  be  requisite  to  make  it  effec- 
tive. Light  gymnastic  and  calisthenic  exercises  should  be 
employed  as  far  as  may  be  necessary  or  suitable  for  the 
general  objects  of  physical  training,  or  as  a  pleasant  and 
beneficial  relaxation  after  the  severer  mental  exercises. 

Where  formal  exercises  in  calisthenics,  etc.,  are  not 
employed,  the  pupils  should  have  sufficient  intermission 
for  recreation  in  the  play-ground.  Time  thus  given  to 
physical  exercise  will  always  prove  a  gain  in  the  exer- 
cise of  the  mental  powers.  When  pupils  are  under 
efficient  discipline,  their  performances,  at  their  lessons, 
are  always  better  after  exercise  in  the  play-ground,— 
for  the  excitement,  as  it  subsides,  leaves  the  intellect 
more  aptive  and  hence  readier  for  class  room  work. 

In  the  case  of  young  pupils,  even  while  in  the  class- 
room, it  is  desirable  that  they  rise  at  intervals  for  a  few 
minutes,  to  exercise,  by  varied  movements,  both  the  up- 
per and  lower  limbs. 

Manners  and  Morals. — Such  instruction  should 
be  given  daily  to  the  pupils  of  all  the  grades  as  will  fos- 
ter a  spirit  of  kindness  and  courtesy  towards  each  other, 
a  feeling  of  respect  toward  parent  and  teacher,  and  a 
love  for  cleanliness,  order,  law,  and  truth.  The  read- 
ing lessons  and  the  ordinary  incidents  of  the  school- 
room may  be  made  the  means  of  inculcating  the  great 
moral  truths  common  to  all  well-ordered  minds. 

Children  learn  to  love  arid  practice  kindness,  neat- 
ness, truthfulness,  and  politeness  by  observing  these 
traits  in  those  around  them.  It  is,  therefore,  exceed- 
ingly important  that  the  teacher  should  present  living 


GENERAL  SUGGESTIONS.  257 

illustrations  of  these  qualities,  by  her  own  conduct  be- 
fore the  pupils,  during  all  her  intercourse  with  the 
class. 

Social  relations,  the  dependence  of  each  individual 
upon  his  neighbor — the  necessity  of  labor — the  benefits 
of  society  and  government,  should  be  illustrated  and 
taught  by  means  of  easy  and  familiar  lessons  suited  to 
the  age  and  capacity  of  the  children.  As  the  develop- 
ment of  the  moral  nature  is  of  greater  importance  to 
the  welfare  of  the  individual  and  the  community  than 
any  other  part  of  education,  no  opportunity  should  be 
omitted  for  training  children  in  such  habits  as  will 
cause  them  to  grow  up  truthful,  honest,  self-governing, 
and  law-abiding  citizens. 


GOVERNMENT  AND  DISCIPLINE. 

In  all  the  rules  and  methods  of  discipline  employed, 
the  true  object  of  discipline  should  steadily  be  kept  in 
view  ;  namely,  to  train  the  pupils  so  that  they  may  form 
right  habits. 

Firmness,  vigilance,  and  uniformity,  in  dealing  with 
children,  are  of  the  first  importance.  The  teacher  should 
never  resort  to  violent  means,  as  pushing,  pulling,  or 
shaking  the  children,  in  order  to  obtain  their  attention. 
All  such  practices  constitute  a  kind  of  corporal  punish- 
ment which,  whether  that  species  of  coercion  be  per- 
mitted or  not,  should  be  most  carefully  avoided. 

Modes  of  punishment  especially  painful  to  the  cor- 
poreal system,  such  as  the  sustaining  of  wearisome  bur- 
dens, unnatural  and  long-continued  attitudes  of  re- 
straint, standing,  kneeling,  etc.,  are  exceedingly  wrong- 
ful and  injurious.  Equally  so  is  the  confining  of  di> 


258  HOW  TO  TEACH. 

linquents,  by  tying  them  or  shutting  them  in  closets. 
These  are  all  a  resort  to  mere  physical  force,  instead  of 
moral  incentives,  and  involve  no  appeal  to  a  sense  of 
honor  or  duty  in  the  child.  They  do  not  properly  as- 
sert the  authority  of  the  teacher,  nor  do  they  really  pro- 
duce obedience  on  the  part  of  the  pupil. 

When  corporal  punishment  is  resorted  to,  it  should 
be  of  a  proper  character — never  partaking  of  that  con- 
tinuous infliction  of  pain  which  we  denominate  torture, 
and  never  administered  except  in  a  spirit  of  mildness, 
and  deep  regret  at  its  necessity.  When  all  those  per- 
suasive incentives  and  agencies  which  constitute 
moral  suasion  have  been  appealed  to  without  avail,  and 
there  is  no  other  recourse,  corporal  punishment  may  be 
resorted  to  in  order  to  save  the  pupil,  but  for  no  other 
reason.  The  necessities  of  discipline  may  seem  to  re- 
quire it,  and  they  certainly  do,  if  in  order  to  meet  them 
the  teacher  must  choose  between  chastising  his  pupil  in 
this  way  and  depriving  him  of  the  benefits  of  the  school 
instruction  and  training,  and  thus  insuring  his  moral 
destruction. 

In  directing  the  various  movements  required  of  the 
pupils,  care  should  be  taken  never  to  touch  them.  The 
teacher  should  take  such  a  position  before  the  class  as 
will  command  the  eye  of  every  pupil,  and  thence  direct 
by  the  voice,  or  by  a  signal.  Pupils  must  be  habituated 
to  the  impression  that  the  teacher  will  give  his  com- 
mands but  once,  and  that  they  must  be  obeyed  at  once. 

Harsh  tones  of  the  voice  are  unnecessary  and  im- 
proper. Words  of  disapprobation  may  be  uttered  by 
the  teacher  in  a  tone  of  decision,  without  the  use  of  any 
severity  that  would  imply  resentment,  anger,  or  antipa- 
thy on  the  part  of  the  teacher.  On  the  contrary,  the 
language  used,  and  the  tones  of  the  voice,  should  al- 


GENERAL  SUGGESTIONS.  259 

ways  express  a  feeling  of  sympathy  with  the  child.  This 
is  the  way  to  win  the  youthful  mind,  and  to  bend  the 
will,  through  the  affections ;  a  different  course  will  an- 
tagonize it,  and  prevent  all  real  submission,  securing 
only  a  temporary  semblance  of  obedience. 

"  As  is  the  teacher,  so  will  be  the  school."  It  is,  there- 
fore, requisite  that  teachers  should  rigidly  discipline 
themselves  by  carefully  cultivating  habits  of  neatness, 
cleanliness,  and  order,  gentleness  of  manner,  a  watchful 
self-control,  and  a  cheerful  spirit.  In  speaking,  let  the 
rising  inflection  of  the  voice  prevail ;  then,  the  falling  in- 
flection of  reproof  Avill  be  more  impressive  and  effectual. 

Teachers  should  seek  to  obtain  the  sympathetic  regard 
of  the  children  by  giving  a  due  attention  to  their  wants 
and  requests,  which  should  be  fulfilled  as  far  as  may  be 
proper  and  reasonable.  Children  are  quick  to  perceive 
and  to  resent  injury  or  injustice.  The  child  who  asks 
for  the  privilege  of  a  drink  of  water,  for  instance,  may  be 
sufferingacutely  ;  and, if  not  accorded  relief,  when  this 
seems  to  be  perfectly  practicable  on  the  part  of  the  teach- 
er, feels  a  sense  of  outrage  which,  for  a  time,  if  not  per- 
manently, impairs  its  respect  and  regard  for  the  teacher. 
The  cultivation  of  a  due  feeling  of  sympathy  for  the 
children  will  wholly  prevent  this.  The  possession  of 
this  feeling  in  its  fullness  is  the  best  foundation  for  suc- 
cess in  both  discipline  and  instruction. 

Encouragement  inspires  confidence;  and  children, 
more  than  others,  need  it.  Let  it  be  given  in  all  cases 
where  this  can  be  honestly  done.  To  a  want  of  this  in 
the  discipline  of  classes,  are  to  be  ascribed  the  timidity 
and  reserve  so  often  manifested  among  pupils  by  a  hes- 
itating manner,  a  low  voice,  and  a  tone  of  inquiry  in 
response,  especially  to  strangers.  A  proper  degree  of 
encouragement  renders  them  confident  and  spirited, 


2GO  J10W  TO  TKACH. 

eager  to  tell  what  they  know,  and  in  an  audible  tone  of 
voice.  Encouragement  has  a  peculiar  influence  in  pro- 
moting both  mental  and  moral  improvement. 

Public  exposures  and  badges  of  disgrace  belong  to  a 
class  of  punishments  which,  if  ever  resorted  to,  should 
be  employed  under  careful  limitations,  and  with  great 
circumspection  and  prudence,  for  it  requires  a  skillful? 
discreet,  and  conscientious  teacher  to  use  them  safely 
and  with  advantage.  In  the  discipline  of  girls,  they 
should  be  avoided  altogether,  as  destructive  of  that  nice 
sense  of  shame  and  that  delicate  sensibility  to  reputa- 
tion which  are  to  be  most  carefully  fostered  in  the  fe- 
male character. 

Cleanliness,  method,  and  regularity  are  among  the 
first  and  most  necessary  elements  of  popular  education. 
Every  rule  requisite  to  maintain  or  impart  these  should 
be  diligently  and  punctiliously  enforced. 

Education  is  unfinished  until  the  physical  powers  are 
brought  into  subjection  to  the  understanding  and  the 
dictates  of  morality  and  social  refinement.  Children 
should  be  taught  how  to  sit,  to  stand,  to  move,  to  walk. 
Rules  are  required  for  this ;  but  they  need  to  be  only  few 
and  simple,  and  the  nice  and  watchful  observation  of 
children  renders  it  quite  easy  to  enforce  them,  provided 
they  are  not  capriciously  applied.  Children  must  first 
be  taught  them,  and  then  never  permitted  to  violate 
them  without  admonition  or  correction. 

Teachers  should  never  forget  that  their  pupils  are 
constantly  and  closely  watching  their  conduct,  and  that 
they  are  prone  to  imitate  whatever  they  observe.  They 
should,  therefore,  see  nothing  that  they  may  not  safely 
imitate.  There  is  an  "unconscious  tuition,"  the  silent 
influence  of  which  produces  the  most  permanent  effects. 

The  character  of  children  is  greatly  affected  by  their 


GENERAL  SUGGESTIONS.  261 

surroundings.  These  should,  therefore,  be  neat  and  or- 
derly. The  rooms  in  which  they  assemble  should  be 
clean,  the  desks  and  other  furniture,  as  far  as  possible, 
without  injury  or  defacement,  and  everything  giving 
evidence  of  constant  and  punctilious  attention.  Chil- 
dren, from  the  contemplation  of  these  things,  uncon- 
sciously acquire  habits  of  order,  neatness,  and  regular- 
ity, which  have  an  important  bearing  upon  their  useful- 
ness and  happiness  in  after  life. 

The  basis  of  goad  order  is  attention.  It  does  not 
require,  that  the  pupils  should  occupy,  for  any  certain 
time,  a  fixed  position  ;  that  they  should  be  compelled 
to  strain  their  glances  upon  a  given  point;  that  they 
should  be  as  motionless  as  statues.  All  this  is  unnatu- 
ral ;  and  Avhatever  is  unnatural  is  really  diwrdcrly. 
The  postures  should  be  graceful,  easy,  and  uniform,  but 
should  be  frequently  changed;  the  movements,  while 
as  simultaneous  as  perfect  attention  would  necessarily 
produce,  should  also  be  easy  and  natural. 

Good  order  involves  impression  rather  than  repres- 
sion ;  it  does  not  consist  in  a  coercion  from  which 
result  merely  silence,  and  a  vacant  gaze  of  painful  re- 
straint, but  it  results  from  the  steady  action  of  awa- 
kened and  interested  intellect, — the  kindling  of  an 
earnest  purpose  and  an  ambition  to  excel.  Hence  by 
making  punishment  the  first,  instead  of  the  last,  resort, 
the  true  object  of  educational  discipline  is  defeated. 
The  prevailing  atmosphere  of  the  class-room  should  be 
always  that  of  kindness  and  love,  equal  to  that  of  a 
parent,  in  whose  place  indeed  the  teacher  is  for  the 
time;  and  it  will  be  almost  in  variably  found  that  every- 
thing essential  to  effective  discipline  will  spring  from 
an  interchange  of  confidence  and  regard  bet \veen  teach- 
ers and  the  pupils  committed  to  their  instruction. 


HOW  TO   TEACH. 

Those  who  have  the  management  and  instruction  of 
our  Common  Schools  should  exercise  the  greatest  care 
that  their  teachings  and  influence  be  not  exclusively  in- 
tellectual,— that  they  tend  not  merely  to  inform  the 
mind,  but  to  form  the  character, — not  only  filling  the 
head,  but  impressing  likewise  the  heart.  Even  where 
the  operations  of  these  schools  are  confined  to  teaching, 
let  the  kind  of  knowledge  and  the  mode  of  imparting 
it  be  dictated  by  considerations  having  in  view  moral 
and  religious,  as  well  as  intellectual,  improvement.  Let 
the  knowledge  imparted  be  always  such  as  will  refine, 
ennoble,  elevate.  "When  scientific  truth  is  presented, 
let  the  pupil  be  led  to  look  not  simply  at  nature,  but 
"  through  nature  up  to  nature's  God ;  "  let  him  learn 
the  laws  and  phenomena  of  the  physical  universe  with 
the  spirit  of  the  Psalmist,  when  he  exclaimed,  "  When 
I  consider  the  heavens,  the  work  of  thy  fingers,  the 
moon  and  the  stars  which  thou  hast  ordained,  what  is 
man,  that  thou  art  mindful  of  him,  and  the  son  of  man 
that  thou  regardest  him  ?  "  Thus  may  instruction  in 
every  class  and  grade  be  made  effectual,  without  the 
dogmatic  teaching  of  sectarian  tenets,  in  subserving  and 
promoting  the  best  interests  of  its  pupils,  both  temporal 
aud  eternal.  Any  scope  or  intention  short  of  this  would 
certainly  be  inconsistent  with  the  intelligence,  as  well 
as  the  moral  and  religious  character  of  our  age  and 
country,  and  must  render  our  Common  School  educa- 
tion, as  a  means  of  fostering  and  supporting  the  free 
institutions  of  our  Eepublic,  unworthy  of  support  or 
vindication. 


GENERAL  SUGGESTIONS. 


A  SCHOOL  LIBRARY. 

tts  Necessity. — Of  all  the  means  necessary  to  a 
teacher's  true  and  lasting  success  in  the  mental  and 
moral  training  of  his  pupils,  few,  if  any,  are  equal  in 
importance  to  a  proper  school  library, — not  necessarily 
a  large  library,  or  an  expensive  one,  but  a  library  con- 
sisting of  interesting  and  instructive  books,  such  as  boys 
and  girls  may  readily  be  led  to  love  to  read. 

The  pernicious  character  of  the  greater  part  of  the 
cheap  literature  found  in  many  so-called  newspapers  and 
in  other  cheap  forms  of  publication,  needs  but  little  com- 
ment. Its  enormous  quantity  shows  that  it  is  extensively 
read,  and  it  is  well  known  that  it  finds  its  chief  market 
among  the  youug.  An  enfeebled  mind  and  a  vitiated 
taste,  as  shown  in  a  craving  for  exciting  and  unnatural 
stories,  and  in  a  positive  dislike  for  instructive  and  truly 
interesting  reading,  as  being  too  tame  and  insipid  to 
hold  the  attention,  are  among  the  common  and  least 
injurious  results  of  an  unchecked  indulgence  in  the  men- 
tal dissipation  which  this  trash  induces.  Its  darker 
shades  and  more  injurious  and  debasing  consequences 
need  not  here  be  dwelt  upon.  The  proper  antidote  and 
substitute  for  this  wide-spread  poison  is  good  reading. 

Such  a  library  is  also  the  indispensable  supplement  to 
the  systematic  mental  instruction  given  in  the  class- 
room. If,  for  instance,  care  be  taken  and  opportunities 
sought  during  the  lessons  in  geography,  history,  or  in 
any  of  the  departments  of  science,  to  introduce  some 
little  book  from  the  library,  and  to  read  a  few  interesting 
paragraphs  illustrating  the  lesson,  a  brief  notice  and 
commendation  of  the  book  at  the  close  of  the  exercise, 
with  a  few  hints  as  to  how  best  to  read  it,  will  utilize 


264  HOW  TO  TEACH. 

many  a  valuable  work  that  might  otherwise  remain  un- 
touched upon  the  shelves. 

Once  introduced  into  the  world  of  good  books,  and 
fairly  interested  in  even  one  of  its  many  departments, — 
once  tasting  and  enjoying  the  wholesome  sweets,  of  a 
sound  and  ennobling  literature,  a  young  man  or  a  young 
woman,  it  may  be  safely  trusted,  will  not  abandon  it  for 
that  to  which  allusion  has  been  made.  A  teacher  has 
failed  in  one  of  the  most  important  of  all  of  his  func- 
tions, if,  being  in  possession  of  a  good  school  library,  he 
has  not  fixed,  in  at  least  some  of  his  pupils,  the  habits 
and  love  of  self-culture,  by  leading  them  to  become 
habitual  readers. 

Its  Character. — Great  care  and  discretion  are  ne- 
cessary in  the  selection  of  books  for  a  school  library.  As 
far  as  possible  they  should  be  small  books.  The  greater 
part  of  the  suitable  works  in  history,  biography,  travels, 
etc.,  are  readily  selected,  and  should  include  such  works 
as  Abbott's  Histories,  Scribner's  Library  of  Wonders  and 
Library  of  Travel,  Chaillu's  works,  the  Rollo  books,  etc., 
together  with  a  fair  proportion  of  good  standard  works, 
such  as  those  of  Prescott,  Bancroft,  Lossing,  Hume,  and 
Macaulay,  the  Student's  Series  ol  Histories,  Translations 
of  Josephus,  Herodotus,  Thucydides,  etc.  In  selecting 
from  the  great  number  of  works  of  imaginary  travel  and 
adventure,  written  with  the  professed  purpose  of  giving 
to  youth  instruction  in  the  physical  geography,  natural 
history,  and  social  condition  of  various  countries,  all 
those  in  which  the  narrative  is  overdrawn,  and  there- 
fore teaches  error,  should  be  rejected.  Natural  history 
and  the  other  subjects  treated  of  in  the  oral  instruction 
in  science,  should  be  abundantly  represented.  If  works 
of  iiction  are  admitted  they  should  be  selected  with  ref- 


GENERAL  SUGGESTIONS.  265 

erence  to  their  moral  purity  aud  their  permanent  value 
as  additions  to  literature,  rather  than  because  they  are 
new  and  are  advertised  as  popular.  Many  a  school  li- 
brary has  been  filled  with  ephemeral  trash  and  made  the 
instrument  of  mental  degradation  rather  than  of  eleva- 
tion, by  want  of  care  in  this  respect.  Such  old  classics 
as  Robinson  Crusoe,  Paul  and  Virginia,  and  the  Vicar 
of  Wakefield,  should  not  be  wanting.  A  few  of  the  lead- 
ing popular  poets  should  also  be  represented  by  small 
volumes.  In  their  selection  of  books,  pupils  should  be 
advised  by  their  teacher,  so  that  they  may  not  attempt 
works  beyond  their  present  ability  to  read  with  profit. 

Uses. — Among  the  many  ways  which  may  be  sug- 
gested for  making  a  systematic  use  of  the  library  as  a 
means  of  culture,  the  following  is  given  as  an  illustration: 

Let  us  suppose  that  some  new  books  have  been  pur- 
chased, and  that  one  of  them  is  Abbott's  Life  of  Madame 
Roland,  and  that  the  teacher  has  himself  first  read  it,  or  at 
least  looked  over  it,  and  marked  a  few  short  but  inter- 
esting passages.  Before  the  class  or  before  several  of 
the  higher  grades  assembled  for  the  purpose,  the  teacher 
hangs  the  map  of  Europe.  In  a  brief  conversational 
lecture  he  states  to  the  class  or  school  a  few  of  the  lead- 
ing points  in  relation  to  France  and  Europe  at  the 
period  referred  to,  then  reads  a  brief  but  interesting 
selection  or  two  from  the  first  portion  of  the  book,  and 
commends  the  book  to  their  notice.  With  such  an 
introduction  many  pupils  will  read  the  work,  while 
without  it  they  would  not  have  thought  of  so  doing. 
It  will  generally  be  found  that  history  and  biography 
are  usually  not  read  by  the  pupils  because  they  have 
none  of  the  preliminary  conceptions  relating  to  the 
subject  which  the  method  above  indicated  supplies. 
12 


266  HOW  TO   TEACH. 

Books  of  travel  present  peculiar  advantages  for  this 
method,  and  are  among  the  most  instructive  portions  of 
current  literature. 

An  excellent  plan  with  individual  and  advanced  pupils 
is  for  the  teacher  to  select  some  interesting  book,  suffi- 
ciently brief  and  simple,  and  in  place  of  the  usual  exer- 
cise in  composition,  to  require  of  the  pupil  an  abstract 
of  limited  length,  with  the  selection  of  a  page  or  two  of 
peculiar  interest  or  importance,  to  be  read  aloud,  with 
such  explanation  or  remarks  as  the  subject  may  suggest 


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[*'] 


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PUBLICATIONS   OF   THE   AMERICAN   BOOK   COMPANY. 


PHYSIOLOGY. 

ECLECTIC   PHYSIOLOGY  AND   HYGIENE.    By  ELI  F. 

BROWN,  M.D.     i2mo,  cloth,  189  pages    .        .        .60  cents 

A  low-priced  text-book,  adapted  to  the  requirements  of  the  new  school  laws 
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FOSTER  &  TRACY'S  PHYSIOLOGY  AND  HYGIENE. 

(Science  Primer  Series.)   By  M.  FOSTER,  M.D.,  and  R.  S.  TRACY, 
M.D.    i8mo,  cloth,  170  pages 35  cents 

Foster's  valuable  work  on  Physiology  is  supplemented  by  the  Chapters  on 
Hygiene  by  Tracy.  This  Primer  is  an  attempt  to  explain  in  the  most  simple 
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The  whole  field  of  physiology  is  not  taken  up,  but  the  fundamental  truths 
are  carefully  set  forth. 

HUNT'S  PRINCIPLES 

M.D.     I2mo,  cloth' 

This  is  an  authoritative  work  on  ,an  qrigtnaK-plan''tehich'  makes  tile  knowl- 
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study  of  anatomy  and  physiology  as  a  means  to  this  end  and  not  the  end  itself. 

The  effects  of  alcoholic  stimulants  and  narcotics  are  treated  in  proper  con- 
nection. No  doubtful  views  are  included. 

JARVIS'S   PHYSIOLOGY  AND    LAWS   OF   HEALTH. 

By  EDWARD  JARVIS,  M.D.     ismo,  cloth,  427  pages      .     $1.20 

A  work  that  approaches  the  subject  with  a  proper  view  of  the  true  object  in 
teaching  physiology  in  schools,  viz.,  that  scholars  may  know  how  to  take  care 
of  their  own  health.  It  makes  the  science  a  secondary  consideration,  and  only 
so  far  as  is  necessary  for  the  comprehension  of  the  laws  of  health. 

HOW  WE   LIVE  ;  or,  The  Human  Body  and  How  to  Take 

Care  of  It.     By  JAMES  JOHONNOT,  EUGENE  BOUTON,  Ph.D., 
and  HENRY  D.  DIDAMA,  M.D 40  cents 

An  Elementary  Course  in  Anatomy,  Physiology,  and  Hygiene.  A  text-book 
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special  attention  to  the  laws  of  hygiene  (including  the  effects  of  alcohol  and 
narcotics  upon  the  human  system),  as  ascertained  from  a  careful  study  of 
anatomy  and  physiology ;  containing  also  a  full  Glossary  of  Terms,  complete 
Index,  etc. 

KELLOGG'S    FIRST    BOOK    IN    PHYSIOLOGY    AND 
HYGIENE.     By  J.  H.  KELLOGG,  M.D.,  170  pages,  40  cents 

The  design  of  this  book  is  to  present  in  as  simple  a  manner  as  possible  such 
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laws  of  healthful  living.  Technical  terms  have  been  avoided,  and  no  matter 
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of  health. 
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PUBLICATIONS  OF  THE  AMERICAN   BOOK   COMPANY. 
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SMITH'S  PRIMER  OF  PHYSIOLOGY  AND  HYGIENE. 

By    WILLIAM    THAYER     SMITH,     M.D.       Cloth,     illustrated, 
124  pages 30  cents 

Designed  for  children.  It  treats  the  subject  in  a  novel  and  interesting 
minner,  and  shows  the  effects  of  stimulants  and  narcotics  on  each  part  or 
function  of  the  body  as  studied. 

SMITH'S  ELEMENTARY  PHYSIOLOGY  AND  HY- 
GIENE. By  WILLIAM  THAYER  SMITH,  M.D.  Full  cloth, 
illustrated,  about  200  pages 50  cents 

This  book  has  been  prepared  with  great  care  to  meet  the  increasing  demand 
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and  inculcating  practical  temperance  by  showing  the  injurious  effects_of  alco- 
holic stimulants  and  narcotics. 

STEELE'S    HYGIENIC    PHYSIOLOGY.     By  J.   DORMAN 

STEELE,  Ph.D.     121110,  cloth,  276  pages         .        .        .     $1.00 

With  especial  reference  to  alcoholic  drinks  and  narcotics.    Throughout  the 

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every  class.     Great  attention  is  given  to  the  subject  of  ventilation,  which  is 

now  attracting  so  much  attention  throughout  the  country. 

STEELE'S  ABRIDGED  HYGIENIC  PHYSIOLOGY.    By 

J.  DORMAN  STEELE,  Ph.D.    i2mo,  cloth,  192  pages,     50  cents 

This  work  embraces  many  of  the  same  excellent  features  as  the  above. 
Adapted  for  younger  pupils. 

THE  ESSENTIALS  OF  ANATOMY,  PHYSIOLOGY, 
AND  HYGIENE.  By  ROGER  S.  TRACY,  M.D.  i2mo, 
299  pages $1.00 

A  clear  and  intelligible  accoant  of  the  structures,  activities  and  care  of  the 
human  system.  Great  prominence  is  given  to  anatomical  and  physiological 
fact.-,  which  are  necessary  preliminaries  to  instruction  in  hygiene. 

HEALTH  LESSONS.  By  JEROME  WALKER,  M.D.  ismo, 
194  pages 48  cents 

The  object  of  this  attractive  little  work  is  to  teach  health  subjects  to  chil- 
dren in  an  interesting  and  impressive  way,  and  to  present  to  their  minds 
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results  in  their  daily  habits  and  observations. 


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